Exam 5: Exponential and Logarithmic Functions

The population of a small country increases according to the function $\mathrm { B } = 2,500,000 \mathrm { e } ^ { 0.02 \mathrm { t } }$ where t is measured in years. How many people will the country have after 3 years?

$4 ^ { x } = 19$ Round to three decimal places.

Does it appear that a linear model or an exponential model is the better fit for the data given in the table below? Explain your choice. 1 6 2 17 3 55 4 160 5 490 6 1450

Match the equation with its graph. - $y = 2 ^ { x + 2 }$

Evaluate the function. Round to two decimal places. -Evaluate $900 ( 0.05 ) ^ { 0.3 ^ { t } } \text { for } t = 0$

Rewrite as a single logarithm. - $\frac { 1 } { 2 } \log _ { 2 } x ^ { 4 } + \frac { 1 } { 4 } \log _ { 2 } x ^ { 4 } - \frac { 1 } { 6 } \log _ { 2 } x$

Provide an appropriate response. -Why is an exponential function one-to-one?

Evaluate the logarithm, if possible. Round the answer to four decimal places. -log 2.81

Use the properties of logarithms to evaluate the expression. - $\ln \mathrm { e } ^ { 8 }$

Find the value of the logarithm without using a calculator. - $\log _ { 9 } \frac { 1 } { 81 }$

Rewrite as a single logarithm. - $\log _ { x } x + \log _ { x } y$

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. 2 27 58 82 13.2 40.5 82.7 172

A company predicts that sales will increase rapidly after a new product is released, with the number of units sold weekly modeled by N $\mathrm { N } = 7000 ( 0.2 ) ^ { 0.5 ^ { t } }$ , where t represents the number of weeks after the product is released. What is the expected upper limit on the number of units sold per week?

Provide an appropriate response. -Consider the Gompertz function $\mathrm{N}=\mathrm{Ca} \mathrm{R}^{\mathrm{t}}, \text { where } 0<\mathrm{R}<1$ . What is the limiting value of this function?

The purchasing power of A dollars after t years of r% inflation is given by the model P $\mathrm { P } = \mathrm { Ae } ^ { - \mathrm { rt } }$ . Assume the inflation rate is currently 6.6%. How long will it take for the purchasing power of $1.00 to be worth $0.67? Round the answer to the nearest hundredth.

Find the value of the logarithm without using a calculator. -ln (l)

The supply function for a certain car is given b $p = 31 \left( 3 ^ { q } \right)$ ) cars, where p dollars is the price per car and q is the quantity of cars, in thousands, supplied at that price. What quantity will be supplied if the price is $67,797 per Car?

The number of periods needed to double an investment when a lump sum is invested at 10%, compounded semiannually, is given by n $\mathrm { n } = \log _ { 1.05 } 2$ Find the number of years before the investment doubles in value, to the Nearest tenth of a year.

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. 1 2 3 4 580 620 670 750

An initial investment of $660 is appreciated for 11 years in an account that earns 1% interest, compounded continuously. Find the amount of money in the account at the end of the period.