Exam 4: Exponential and Logarithmic Functions

Choose the one alternative that best completes the statement or answers the question. -The logistic growth function $f ( t ) = \frac { 800 } { 1 + 9.0 \mathrm { e } ^ { - 0.16 t } }$ describes the population of a species of butterflies $t$ months after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 15 months?

Find the amount that results from the investment. - $\$ 1,000$ invested at $6 \%$ compounded annually after a period of 8 years

Find the domain of the function. - $f ( x ) = 2 - \ln ( 3 x )$

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -5.5% compounded quarterly

Solve the equation. - $\log ( 5 + x ) - \log ( x - 4 ) = \log 2$

Choose the one alternative that best completes the statement or answers the question. Find the effective rate of interest. -12.25% compounded monthly

Choose the one alternative that best completes the statement or answers the question. -The Feldmans bought their first house for $14,000. Over the years they moved three times into bigger and bigger houses. Now, 41 years later, they are ready to retire and want a smaller house like the first one they Bought. If inflation in property values has averaged 3.6% per year during that time, how much will such a House cost them now? (Round your answer to the nearest dollar.)

Decide whether or not the functions are inverses of each other. - $f ( x ) = \sqrt { x + 7 }$ , domain $[ - 7 , \infty ) ; g ( x ) = x ^ { 2 } + 7$ , domain $( - \infty , \infty )$

Find the domain of the function. - $f ( x ) = \log _ { 9 } ( x + 8 ) ^ { 2 }$

Find functions f and g so that f ° g = H. - $H ( x ) = \left( 5 - 2 x ^ { 3 } \right) ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\log _ { 5 } x = 2$

Find the present value. Round to the nearest cent. -To get $2000 after 10 years at 9% compounded semiannually

Express as a single logarithm. - $3 \log _ { b } q - \log _ { b } r$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { \pi } 37 = x$

Choose the one alternative that best completes the statement or answers the question. -Tracey bought a diamond ring appraised at $1,700 at an antique store. If diamonds have appreciated in value at an annual rate of 10%, what was the value of the ring 10 years ago? (Round your answer to the nearest dollar.)

Solve the equation. - $3 ^ { - x } = \frac { 1 } { 9 }$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. -The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function $M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) \text {, where } x _ { 0 } = 10 ^ { - 3 }$ What would be the readings x (to the nearest tenth) for magnitudes of 4.5 and 7.5?

Choose the one alternative that best completes the statement or answers the question. Find the domain of the composite function f ° g. - $f ( x ) = \sqrt { x - 1 } ; g ( x ) = \frac { 1 } { x - 8 }$

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln \sqrt { 17 }$

Change the logarithmic expression to an equivalent expression involving an exponent. - $\log _ { 1 / 3 } 9 = - 2$