Exam 3: Exponential, Logistic, and Logarithmic Functions

Solve the problem. -Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after x years can be described by $A ( x ) = 100 \mathrm { e } ^ { - 0.01828 x }$ . How much is remaining after 50 years? Round the answer to the nearest hundredth of a milligram.

Find the domain of the function. - $f ( x ) = \log _ { 10 } \left( x ^ { 2 } - 11 x + 18 \right)$

Provide an appropriate response. -The function $f ( x ) = 200 \frac { ( 1 + 0.06 / 4 ) ^ { x } - 1 } { 0.06 / 4 }$ describes the future value of a certain annuity. How many payments per year are there?

Match the function f with its graph. - $f ( x ) = \log _ { 4 } ( x ) + 4$

Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. - $f ( x ) = 7 \cdot 1.09 x$

Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. - $7 \log _ { m } q - 8 \log _ { m } z ^ { 2 }$

Solve the equation. - $e ^ { x } - 9 = \frac { - 14 } { e ^ { X } }$

Graph the function and analyze it for domain, range, continuity, increasing or decreasing behavior, asymptotes, and end behavior. - $f ( x ) = \ln \left( x ^ { 2 } \right)$

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

Find the domain of the function. - $f ( x ) = \log _ { 10 } \frac { x + 4 } { x - 4 }$

Write the expression using only the indicated logarithms. - $\log _ { 1 / 6 } ( a - b )$ using common logarithms

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 8.2 } 7.0$

Simplify the expression. - $15 \log _ { 15 } 18$

Solve the equation by changing it to exponential form. - $\log x = 7.1$

Find the exact solution to the equation. - $2 \cdot 3 ^ { x / 2 } = 54$

Use the change of base rule to find the logarithm to four decimal places. - $\log _ { 9 } 0.94$

Solve the problem. -Find the periodic payment of a loan with present value $20,000 and an annual interest rate 6.3% for a term of 3 years, with payments made and interest charged 12 times per year.

Match the function with its graph. -f(x) = 4log x

Find the logistic function that satisfies the given conditions. -Initial population $= 6$ , maximum sustainable population $= 18$ , passing through $( 1,13 )$

Solve the problem. -Find how long it will take for $8600 invested at 9.325% per year compounded daily to triple in value. Find the answer to the nearest year.