Exam 9: Exponential and Logarithmic Functions

Solve the problem. -The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential Growth modelel $\mathrm { A } = 8000 \mathrm { e } ^ { 0.045 \mathrm { t } }$ . H. ow much did you initially invest in the account?

Solve the problem. -Four bacteria are placed in a petri dish. The population will triple every day. The formula for the number of bacteria in the dish on day t is $\mathrm { N } ( \mathrm { t } ) = 4 ( 2 ) ^ { \mathrm { t } }$ where t is the number of days after the four bacteria are placed in the dish. How many bacteria are in the dish Eight days after the four bacteria are placed in the dish?

Evaluate. - $\log _ { 4 } \frac { 1 } { 64 }$

Write as a logarithm of a single expression. - $4 \log _ { b } m - \log _ { b } n$

Solve the problem. -The expected future population of a small town, which currently has 7900 residents, can be approximated by the formula $y = 7900 ( 1.8 ) ^ { - 0.2 t }$ where t is the number of years in the future. Find the expected population of the town 30 years in the future.

Use the change of base formula to find the value of the following logarithm. Do not round logarithms in the change of base formula. Write the answer rounded to the nearest ten-thousandth. - $\log _ { 24 } 311$

Find the value of N. Round to three decimal places. -ln N = -1.3

For the given functions f and g , find the indicated composition. - f(x)=+6,g(x)=-6 (f\circg)(x)

For the given functions f and g , find the indicated value. - f(x)=-2x+4,g(x)=-2x-5 (f\circg)(-4)

Determine whether the function is a one-to-one function. - $y = | x + 3 |$

Find the common logarithm of the number. Round answer to four decimal places. -log 3.33

Find the value of N. Round to three decimal places. -ln N = 0.9474

For the given functions f and g , find the indicated value. - $f ( x ) = x ^ { 2 } + 5 x , \quad g ( x ) = x + 4$ $( f \circ g ) ( 2 )$

Graph the function. - $f ( x ) = 5 ^ { x - 1 }$

Evaluate. - $\log 10 ^ { - 3 }$

Solve the problem. -A sample of 1000 g of lead-210 decays to polonium-210 according to the function given by $\mathrm { A } ( \mathrm { t } ) = 1000 ( 2.718 ) ^ { - 0.032 t } ,$ where t is time in years. What is the amount of the sample, to the nearest gram, after 40 years?

Write the equation in logarithmic form. - $\left( \frac { 1 } { 5 } \right) ^ { 2 } = \frac { 1 } { 25 }$

Evaluate. - $\frac { 1 } { 4 } \log _ { 9 } \sqrt [ 5 ] { 9 }$

The following equation is in the forming equation is in the form $\mathrm { P } = \mathrm { P } _ { 0 } \mathrm { e } ^ { \mathrm { kt } }$ . Solve the equation for the remaining variable. Remember, e is a constant. - $65 = 150 \mathrm { e } ^ { - 0.01 t }$

Solve the problem. -Alicia invests $14,000 in a savings account earning interest at a rate of 9% compounded semiannually. Find the amount in the account at the end of 7 years.