Exam 4: Exponential Functions

Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of $0.27 \%$ per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.

(Short Answer)

4.9/5

(37)

Question 81

A quantity decreased from 100 to 95 . By what percentage did it decrease?

(Short Answer)

4.7/5

(36)

Question 82

The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is $g(x)=\ldots(\ldots)^{x}$ . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places. $The following figure shows two functions, one linear and the other exponential. The formula for the linear one is f(x) =-----------+------------x, and the formula for the exponential one is g(x)=\ldots(\ldots)^{x} . Round the first two answers to 2 decimal places and the last two answers to 3 decimal places.$

(Short Answer)

4.8/5

(30)

Question 83

You invest $\$ 6,000$ in an account earning $2.6 \%$ annual interest, compounded continuously. After how many years is the investment worth $\$ 12,000$ ? Round your answer to two decimal places, if necessary.

(Short Answer)

4.9/5

(39)

Question 84

Find $\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x}$ . For $\infty$ or $-\infty$ , enter "inf" or "-inf".

(Short Answer)

4.8/5

(30)

Question 85

The graph of the exponential function $P(t)$ is shown below. Suppose $P(t)$ represents a city's population, in thousands, $t$ years after 1995. Which of the following quantities are equivalent?

(Multiple Choice)

4.9/5

(37)

Question 86

In the exponential formula $Q=47,200(0.9)^{t}$ , if $Q=a(1+r)^{t}$ then $r=\ldots \%$ .

(Short Answer)

4.9/5

(29)

Question 87

In some developing countries, the inflation rate has been as high as $0.94 \%$ per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.

(Short Answer)

4.9/5

(44)

Question 88

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is linear.

(Short Answer)

4.8/5

(40)

Question 89

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ per year. What is the formula for $P(t)$ , the population for the United States $t$ years after 2005?

(Multiple Choice)

4.7/5

(38)

Question 90

What is the horizontal asymptote of $y=87(0.64)^{t}$ as $t \rightarrow \infty$ ?

(Multiple Choice)

4.9/5

(46)

Question 91

The figure below shows the graphs of the following functions: (A) $y=e^{t}$ (B) $y=2^{t}$ (C) $y=e^{-t}$ (D) $y=2^{-t}$ $The figure below shows the graphs of the following functions: (A) y=e^{t} (B) y=2^{t} (C) y=e^{-t} (D) y=2^{-t} Which one is the graph of A?$ Which one is the graph of A?

(Short Answer)

4.7/5

(35)

Question 92

The formula for the exponential function $P$ such that $P(11)=10$ and $P(12)=9$ is given by $P(t)=\ldots(\ldots)^{t}$ . Give both answers to 3 decimal places.

(Short Answer)

5.0/5

(29)

Question 93

The price of an item increases due to inflation. Let $p(t)=22.50(1.037)^{t}$ be the price of the item as a function of time in years, with $t=0$ in 2004. What is the weekly inflation rate? Round to 2 decimal places.

(Short Answer)

4.9/5

(29)

Question 94

Showing 81 - 94 of 94

Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of $0.27 \%$ per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.

A quantity decreased from 100 to 95 . By what percentage did it decrease?

You invest $\$ 6,000$ in an account earning $2.6 \%$ annual interest, compounded continuously. After how many years is the investment worth $\$ 12,000$ ? Round your answer to two decimal places, if necessary.

Find $\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x}$ . For $\infty$ or $-\infty$ , enter "inf" or "-inf".

The graph of the exponential function $P(t)$ is shown below. Suppose $P(t)$ represents a city's population, in thousands, $t$ years after 1995. Which of the following quantities are equivalent?

In the exponential formula $Q=47,200(0.9)^{t}$ , if $Q=a(1+r)^{t}$ then $r=\ldots \%$ .

In some developing countries, the inflation rate has been as high as $0.94 \%$ per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is linear.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ per year. What is the formula for $P(t)$ , the population for the United States $t$ years after 2005?

What is the horizontal asymptote of $y=87(0.64)^{t}$ as $t \rightarrow \infty$ ?

The figure below shows the graphs of the following functions: (A) $y=e^{t}$ (B) $y=2^{t}$ (C) $y=e^{-t}$ (D) $y=2^{-t}$ $The figure below shows the graphs of the following functions: (A) y=e^{t} (B) y=2^{t} (C) y=e^{-t} (D) y=2^{-t} Which one is the graph of A?$ Which one is the graph of A?

The formula for the exponential function $P$ such that $P(11)=10$ and $P(12)=9$ is given by $P(t)=\ldots(\ldots)^{t}$ . Give both answers to 3 decimal places.

The price of an item increases due to inflation. Let $p(t)=22.50(1.037)^{t}$ be the price of the item as a function of time in years, with $t=0$ in 2004. What is the weekly inflation rate? Round to 2 decimal places.

Linear Functions and Change

Functions

Quadratic Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

Exam 4: Exponential Functions

Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of 0.27%0.27 \%0.27% per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.

A quantity decreased from 100 to 95 . By what percentage did it decrease?

You invest $6,000\$ 6,000$6,000 in an account earning 2.6%2.6 \%2.6% annual interest, compounded continuously. After how many years is the investment worth $12,000\$ 12,000$12,000 ? Round your answer to two decimal places, if necessary.

Find lim⁡x→−∞7.2e0.11x\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x}limx→−∞​7.2e0.11x . For ∞\infty∞ or −∞-\infty−∞ , enter "inf" or "-inf".

The graph of the exponential function P(t)P(t)P(t) is shown below. Suppose P(t)P(t)P(t) represents a city's population, in thousands, ttt years after 1995. Which of the following quantities are equivalent?

In the exponential formula Q=47,200(0.9)tQ=47,200(0.9)^{t}Q=47,200(0.9)t , if Q=a(1+r)tQ=a(1+r)^{t}Q=a(1+r)t then r=…%r=\ldots \%r=…% .

In some developing countries, the inflation rate has been as high as 0.94%0.94 \%0.94% per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.

Let f(x)f(x)f(x) be given in the table below. Find the value of kkk if f(x)f(x)f(x) is linear.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of 1.34%1.34 \%1.34% per year. What is the formula for P(t)P(t)P(t) , the population for the United States ttt years after 2005?

What is the horizontal asymptote of y=87(0.64)ty=87(0.64)^{t}y=87(0.64)t as t→∞t \rightarrow \inftyt→∞ ?

The figure below shows the graphs of the following functions: (A) y=ety=e^{t}y=et (B) y=2ty=2^{t}y=2t (C) y=e−ty=e^{-t}y=e−t (D) y=2−ty=2^{-t}y=2−t Which one is the graph of A?

The formula for the exponential function PPP such that P(11)=10P(11)=10P(11)=10 and P(12)=9P(12)=9P(12)=9 is given by P(t)=…(…)tP(t)=\ldots(\ldots)^{t}P(t)=…(…)t . Give both answers to 3 decimal places.

The price of an item increases due to inflation. Let p(t)=22.50(1.037)tp(t)=22.50(1.037)^{t}p(t)=22.50(1.037)t be the price of the item as a function of time in years, with t=0t=0t=0 in 2004. What is the weekly inflation rate? Round to 2 decimal places.

Linear Functions and Change

Functions

Quadratic Functions

Logarithmic Functions

Transformations of Functions and Their Graphs

Trigonometry and Periodic Functions

Triangle Trigonometry and Polar Coordinates

Trigonometric Identities, Models, and Complex Numbers

Compositions, Inverses, and Combinations of Functions

Polynomial and Rational Functions

Vectors and Matrices

Sequences and Series

Parametric Equations and Conic Sections

Filters

Suppose the amount of ozone in the atmosphere is decreasing exponentially at a continuous rate of $0.27 \%$ per year. How many years will it take before one-third of the ozone has disappeared? Round to the nearest year.

You invest $\$ 6,000$ in an account earning $2.6 \%$ annual interest, compounded continuously. After how many years is the investment worth $\$ 12,000$ ? Round your answer to two decimal places, if necessary.

Find $\lim _{x \rightarrow-\infty} 7.2 e^{0.11 x}$ . For $\infty$ or $-\infty$ , enter "inf" or "-inf".

The graph of the exponential function $P(t)$ is shown below. Suppose $P(t)$ represents a city's population, in thousands, $t$ years after 1995. Which of the following quantities are equivalent?

In the exponential formula $Q=47,200(0.9)^{t}$ , if $Q=a(1+r)^{t}$ then $r=\ldots \%$ .

In some developing countries, the inflation rate has been as high as $0.94 \%$ per day. What is the corresponding percent annual inflation rate? Round to the nearest whole number.

Let $f(x)$ be given in the table below. Find the value of $k$ if $f(x)$ is linear.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ per year. What is the formula for $P(t)$ , the population for the United States $t$ years after 2005?

What is the horizontal asymptote of $y=87(0.64)^{t}$ as $t \rightarrow \infty$ ?

The figure below shows the graphs of the following functions: (A) $y=e^{t}$ (B) $y=2^{t}$ (C) $y=e^{-t}$ (D) $y=2^{-t}$ $The figure below shows the graphs of the following functions: (A) y=e^{t} (B) y=2^{t} (C) y=e^{-t} (D) y=2^{-t} Which one is the graph of A?$ Which one is the graph of A?

The formula for the exponential function $P$ such that $P(11)=10$ and $P(12)=9$ is given by $P(t)=\ldots(\ldots)^{t}$ . Give both answers to 3 decimal places.

The price of an item increases due to inflation. Let $p(t)=22.50(1.037)^{t}$ be the price of the item as a function of time in years, with $t=0$ in 2004. What is the weekly inflation rate? Round to 2 decimal places.