Exam 4: Exponential and Logarithmic Functions

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = x ^ { 3 } + 1 , g ( x ) = \sqrt [ 3 ] { x - 1 }$

For the given functions f and g, find the requested composite function. -f(x) = 5x + 10, g(x) = 5x - 1; Find (f °g)(x).

Use a calculator to find the natural logarithm correct to four decimal places. - $\ln 49,800,000$

Solve the problem. -A local bank advertises that it pays interest on savings accounts at the rate of 3% compounded monthly. Find the effective rate. Round answer to two decimal places.

Solve the problem. -If $5 ^ { x } = 6$ , what does $5 ^ { - 2 x }$ equal?

Solve the equation. - $\log _ { a } ( x - 7 ) - \log _ { a } ( x - 2 ) = \log _ { a } ( x - 4 ) - \log _ { a } ( x + 12 )$

The graph of a logarithmic function is shown. Select the function which matches the graph. - A) $y = \log ( - x )$ B) $y = \log ( x )$ C) $y = - \log ( - x )$ D) $y = - \log ( x )$

Solve the problem. -The half-life of radium is 1690 years. If 150 grams is present now, how long (to the nearest year) till only 100 grams are present?

Solve the problem. -Instruments on a satellite measure the amount of power generated by the satellite's power supply. The time t and the power P can be modeled by the function P $\mathrm { P } = 50 \mathrm { e } ^ { - \mathrm { t } / 300 }$ , where t is in days and P is in watts. How much power will be available after 378 days? Round to the nearest hundredth.

Write the word or phrase that best completes each statement or answers the question. - $\frac { e ^ { x } - e ^ { - x } } { 2 } = - 1$

Solve the problem. -models the average number of free-throws a basketball player can make consecutively during practice as a function of time, where x is the number of consecutive days the basketball Player has practiced for two hours. After 13 days of practice, what is the average number of consecutive free Throws the basketball player makes?

Solve the problem. -What principal invested at 6%, compounded continuously for 3 years, will yield $1500? Round the answer to two decimal places.

Use transformations to graph the function. Determine the domain, range, and vertical asymptote of the function. - $h(x)=3+\log (x+4)$

Graph the function. - $f ( x ) = e ^ { x }$ A) B) C) D)

Find the exact value of the logarithmic expression. -ln $\mathrm { e }$

Determine i) the domain of the function, ii) the range of the function, iii) the domain of the inverse, and iv) the range of the inverse. - $f ( x ) = - 7 x - 4$

Find functions f and g so that f $f \circ g = H$ - $\mathrm { H } ( \mathrm { x } ) = | 3 \mathrm { x } + 7 |$

Find the effective rate of interest. -12% compounded continuously

Decide whether the composite functions, f $f \circ g$ nd $\mathbf { g } \circ \mathrm { f }$ f, are equal to x. - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Solve the problem. -The temperature (in degrees Fahrenheit) of a dead body that has been cooling in a room set at 70° is measured as 88°. One hour later, the body temperature is 87.5°. How long (to the nearest hour) before the first measurement was the time of death, assuming that the body temperature of the deceased at the time of death was 98.6°. Assume the cooling follows Newton's Law of Cooling: $\mathrm { U } = \mathrm { T } + \left( \mathrm { U } _ { \mathrm { O } } - \mathrm { T } \right) \mathrm { e } ^ { \mathrm { kt } }$