Exam 4: Exponential Functions

What is $\lim _{t \rightarrow-\infty}\left(14+5 e^{4 t-1}\right)$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

A population has size 3,500 at time $t=0$ , with $t$ in years. If the population grows by 80 people per year, what is the formula for $P$ , the population at time $t$ ?

Let $P(t)=5,000 e^{0.037 t}$ give the size of a population of animals in year $t$ . After how many years will the population be approximately 10,099 ? Round to the nearest year.

Match the graph to its equation.

Is the formula for a function representing a quantity which begins at $N$ in year $t=0$ and grows at a constant annual rate of $r \%$ given by $f(t)=r(1+N)^{t} ?$

What is the growth factor if sales increase by $37 \%$ each month?

Find a possible formula for the exponential function $f$ such that the points $(5,2684.355)$ and $(3,262.144)$ are on the graph.

Jeff has $\$ 40,000$ . He placed $\$ 20,000$ in Bank 1 with an account earning $3.4 \%$ annual interest, compounded continuously. He also placed \$20,000 in Bank 2 with an account earning 3.6\% annual interest compounded weekly. After 10 years, A) how much money is in Bank 1 ? B) how much money is in Bank 2?

Which of the graphs in the following figure is the graph of $150(1.1)^{t}$ ?

The amount of pollution in a harbor $t$ hours after it was contaminated by illegal dumping is given by $A=50(0.8)^{t}$ tons. After how many hours is there less than 10 tons of pollution in the harbor? Round to 1 decimal place.

A biologist measures the amount of contaminant in a lake 3 hours after a chemical spill and again 11 hours after the spill. She sets up two possible models to determine $Q$ , the amount of the chemical remaining in the lake as a function of $t$ , the time in hours since the spill. The first model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 7 tons\hour. Using this model, she estimates that the lake will be free from the contaminant 24 hours after the spill. The second model assumes that the amount of contaminant decreases exponentially. She measures the spill a third time after 23 hours and finds that 44 tons remain. Which model seems best?

Is the function graphed exponential?

The following figure gives the graph of $C=f(t)$ , where $\mathrm{C}$ is the computer hard disk capacity (in hundreds of megabytes) that could be bought for $\$ 500 t$ years past 1989 . If the trend displayed in the graph continued, in what year would the capacity that can be bought for $\$ 500$ be 4,600 ? $C \text {, capacity (in } 100 \text { s of megabytes) }$

Each of the functions in the table below is increasing, but each increases in a different way. One is linear, one is exponential, and one is neither. The formula for the exponential one is $\ldots(\ldots)^{t}$ Round your second answer to 2 decimal places.

The US population in 2005 was approximately 296.4 million. Assume the population increases at a rate of $1.34 \%$ per year. Some demographers believe that the ideal population of the United States is about 130 million. According to this model, in what year did this occur?

A biologist measures the amount of contaminant in a lake 2 hours after a chemical spill and again 15 hours after the spill. She sets up a possible model to determine $Q$ , the amount of the chemical remaining in the lake as a function of $t$ , the time in hours since the spill. The model assumes the contaminant is leaving the lake at a constant rate, which she determines to be 6 tons\hour. She estimates that the lake will be free from the contaminant 35 hours after the spill. How many tons of the contaminant were in the lake at the 15 hour reading?

What is $\lim _{x \rightarrow \infty} e^{-4 x}$ ? If necessary, enter "inf" for $\infty$ and "-inf" for $-\infty$ .

An ant population grows at a continuous growth rate of $11.3 \%$ . If the population starts with 22,000 ants, how many ants are there after 6 months? Round your answer to the nearest ant.

The price of an item increases due to inflation. Let $p(t)=22.50(1.029)^{t}$ give the price of the item as a function of time in years, with $t=0$ in 2004. What is the practical interpretation of $p^{-1}(70)$ ?