Exam 5: Exponential and Logarithmic Functions

In the formula A(t) A ( t ) = A _ { n e ^{k t}> } , A is the amount of radioactive material remaining from an initial amount A0 at a given time t, and k is a negative constant determined by the nature of the material. An artifact is discovered at a Certain site. If it has 59% of the carbon-14 it originally contained, what is the approximate age of the artifact? Carbon-14 decays at the rate of 0.0125% annually. Round to the nearest year, if necessary.

June made an initial deposit of $4700 in an account for her son. Assuming an interest rate of 8% compounded quarterly, how much will the account be worth in 12 years?

$2 ( x - 3 ) = 17$ Round to three decimal places.

Find the exponential function that models the data in the table below. () -2 22 -1 15.4 0 10.78 1 7.546 2 5.2822

Determine whether or not the given function is an exponential function. - $y = x ^ { 7 } + 9 x$

$400 \left[ \frac { 1.06 ^ { n } - 1 } { 0.07 } \right]$ for $n = 221$

Write the logarithmic equation in exponential form. - $2 y = \ln ( - 8 x )$

Evaluate the function. Round to two decimal places. -Evaluate $700 ( 0.03 ) ^ { 0.2 ^ { t } } \text { for } t = 10$

Find the function value. - $\text { Let } f ( x ) = 3 ^ { x } \text {. Find } f ( 2 )$

Find the value of the logarithm without using a calculator. - $\log _ { 9 } \frac { 1 } { 729 }$

Find the amount of money in an account after 10 years if $2100 is deposited at 4% annual interest compounded annually.

The sales of a new product (in items per month) can be approximated by $S ( x ) = 400 + 300 \log ( 3 t + 1 )$ , where t represents the number of months after the item first becomes available. Find the number of items sold per Month 33 months after the item first becomes available.

Find the logarithmic function that models the data in the table below. 1 2 3 4 5 1.3 4.9 6.8 8.0 9.2

Explain why this sequence of steps is incorrect: 64 =[(-8)(-8)] =(-8)+(-8)

A certain radioactive isotope has a half-life of approximately 950 years. How many years to the nearest year would be required for a given amount of this isotope to decay to 75% of that amount?

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log 5 x = 3$

Under ideal conditions, a population of rabbits has an exponential growth rate of 11.6% per day. Consider an initial population of 400 rabbits. Find the exponential growth function.

Determine whether or not the given function is an exponential function. - $y = 6 x ^ { e }$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - 5 ln x=8

Evaluate. Round dollar amounts to the nearest cent and other answers to the nearest thousandth when necessary. - $\mathrm { P } \left( 1 + \frac { \mathrm { r } } { \mathrm { k } } \right) ^ { \mathrm { kn } } \text { for } \mathrm { P } = \$ 1,000 , \mathrm { n } = 6 , \mathrm { r } = 7 \% \mathrm { k } = 1$