Exam 9: Exponential and Logarithmic Functions

Solve. -Calculate how much money Ronnie has after 3 years if he originally invested $\$ 4879$ at $7.6 \%$ compounded continuously. Use $\mathrm { A } = \mathrm { Pe } ^ { \mathrm { rt } }$ , where $\mathrm { A }$ is the final amount, $\mathrm { P }$ is the original amount deposited, $\mathrm { r }$ is the interest rate, and $t$ is the number of years.

Solve the equation. - $\log _ { 2 } x = 5$

Solve. Round the answer to the nearest whole. -The size of the rat population of a wharf area grows at a rate of 7% monthly. If there are 300 rats in June, find how many rats should be expected by next June.

Find the exact value. - $\log 10 ^ { 7 }$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( - 7 , - 8 ) , ( 8,7 ) , ( 1,1 ) , ( - 1 , - 1 ) \}$

Solve the equation for x. Give an exact solution. - $\ln 7 x = 3$

Find the inverse of the one-to-one function. - $f ( x ) = x ^ { 3 } + 2$

Determine whether the function is a one-to-one function. - $\mathrm { f } = \{ ( - 3,17 ) , ( - 4 , - 5 ) , ( - 18,19 ) \}$

Graph the function and its inverse on the same set of axes. - $f ( x ) = - 2 x + 1$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 3 } - 5 x ; g ( x ) = - 3 x$ Find $( g \circ f ) ( x )$ .

Graph the function and its inverse on the same set of axes. - $f(x)=4 x$

Use a calculator to approximate the logarithm to four decimal places. - $\log 0.00235$

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$ $\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$ - $\log _ { b } \frac { 3 } { 8 }$

Solve. -A city is growing at the rate of 0.8% annually. If there were 3,917,000 residents in the city in 1994, find how many (to the nearest ten-thousand) are living in that city in 2000 $\text { Use } y = 3,917,000 ( 2.7 ) ^ { 0.008 t } \text {. }$

Write the function F(x) as a composition of f, g, or h. - f(x)=+6g(x)=7xh(x)= F(x)=

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $3 \log _ { x } 3 + \log _ { x } 2$

Write as a logarithmic equation. - $10 ^ { 4 } = 10,000$

Graph the function. - $y=\log _{2} x$

Find the exact value. - $\ln e ^ { 6.9 }$

Use the exponential decay formula with half-lives to find the final amount. Round to the nearest tenth when necessary. - Original Amount Half-Life (in years) Number of Years Final Amount after x Time Intervals 500 15 45