Exam 8: Exponential and Logarithmic Functions and Applications

A department store credit card advertises no payments for 2 years on purchases. What they do not advertise is that interest is compounded continuously for those two years at an annual rate of 19.7%. If you make a purchase of $550 and make no payments for 2 years, how much would you owe at the End of those 2 years?

Solve the exponential equation by using the property that bx = by implies x = y, for b > 0 and b≠ 1. $8 ^ { 2 x } = 64 ^ { x ^ { 2 } }$

If $f ( x ) = 15 x + 7$ and $g ( x ) = x ^ { 2 } - 5 x$ , find $( f + g ) ( x )$ .

Carbon dating determines the approximate age of an object made from materials that wereonce alive by measuring the remaining percentage of a radioactive isotope, carbon-14. The age is calculated Using the formula $A = - \frac { \ln P } { 0.000121 }$ where P is the percentage of remaining carbon-14 (in decimal form). The Shroud of Turin was Found to have 92.5% of its carbon-14 remaining in the 1980's. How old was it at the time? Round To the nearest year.

In 2000, the population of Sheboygan, WI was about 113,000 and was growing at a rate of 0.85% per year. Find an exponential function that describes the population P in terms of t, the number of Years after 2000.

Expand into sums and/or differences of logarithms. Assume all variables represent positive real numbers. $\log \sqrt [ 3 ] { \frac { a ^ { 2 } b ^ { 3 } } { c ^ { 5 } } }$

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\log _ { 5 } 100 + \log _ { 5 } 2 - \log _ { 5 } 8$

Evaluate the expression by using a calculator. Round to 4 decimal places. $7 ^ { - \pi }$

The level of a sound in decibels is calculated using the formula $D = 10 \cdot \log \left( I \times 10 ^ { 12 } \right)$ where I is the intensity of the sound waves in watts per square meter. The softest sound that a human can hear has an intensity of 10-12 watts per square meter. How many decibels is that?

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $\log _ { 19 } x ^ { 7 } y ^ { 8 } - \log _ { 19 } x ^ { 5 } y ^ { 9 }$

Write the equation in exponential form. $\log _ { 17 / 5 } 1 = 0$

Solve the logarithmic equation. $\log x = 1 - \log ( x + 3 )$

Compare the expressions by approximating their values on a calculator. Which two expressions are equivalent? I. $\log \left( \frac { 9 } { 7 } \right)$ II. $\frac { \log 9 } { \log 7 }$ III. $\log 9 - \log 7$

Evaluate without the use of a calculator. $\log _ { 2 / 3 } \frac { 8 } { 27 }$

Approximate the function value from the graph. $(f \circ g)(4)$

Evaluate the expression. $\log _ { y } y ^ { 7 }$

Graph y = f (x). $f ( x ) = \log _ { 1 / 3 } x$

A rumor begins to spread across a college campus. The amount of time in days that it takesthe number of people that have heard it to double is given by $D = \frac { \ln 2 } { r / 7 }$ where r is the rate of the spread of the rumor per week. If a particular rumor is spreading at a rate of 28% per week, how long is the doubling time? Round to the nearest tenth of a day.

Write the expression as a single logarithm. Assume all variables represent positive real numbers. $2 \log ( x + 6 ) + \frac { 1 } { 3 } \log y - 5 \log z$

Use the change-of-base formula to approximate the logarithm to three decimal places. $\log _ { 3 / 5 } \left( \frac { 1 } { \sqrt { 6 } } \right)$