Exam 5: Exponential and Logarithmic Functions

Tasha borrowed $11,000 to purchase a new car at an annual interest rate of 11%. She is to pay it back in equal monthly payments over a 3 year period. What is her monthly payment?

Provide an appropriate response. -Why can' $y = 2 ^ { x } \text { have an } x \text {-intercept }$

What is the domain of the function $y = \left( \frac { 1 } { 8 } \right) ^ { x }$ ?

Determine if the function is a growth exponential or a decay exponential. - $y = 3 ^ { 0.7 x }$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. -log (x-9)=1-log x

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - log (x+20)=1

Find the present value of a loan with an annual interest rate of 6.5% and periodic payments of $1270.74 for a term of 27 years, with payments made and interest charged 12 times per year.

Evaluate the logarithm, if possible. Round the answer to four decimal places. -ln 0.000873

Explain the error in the following: $\log _ { 4 } 3 y = \log _ { 4 } 3 \cdot \log 4 y$

Find the exponential function that satisfies the given conditions. -Initial value $= 36$ , increasing at a rate of $13 \%$ per year

If $4900 is invested in an account earning 7% annual interest compounded continuously, then the number of years that it takes for the amount to grow to $9800 is $\mathrm { n } = \frac { \ln 2 } { 0.07 }$ Find the number of years to the nearest tenth of a Year.

Assume the cost of a gallon of milk is $2.60. With continuous compounding, find the time it would take the cost to be 4 times as much (to the nearest tenth of a year), at an annual inflation rate of 6%.

If an earthquake has an intensity of I, then its magnitude, as computed by the Richter Scale, is given by $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$ , where $\mathrm { I } _ { 0 }$ is the intensity of a small, measurable earthquake. (Consider $\mathrm { I } _ { 0 } = 1$ for this question.) If one earthquake has a magnitude of $3.0$ on the Richter scale and a second earthquake has a magnitude of $8.5$ on the Richter scale, how many times more intense (to the nearest whole number) is the second earthquake than the first?

The pH of a solution is given by the formula $\mathrm { pH } = - \log \left[ \mathrm { H } ^ { + } \right] , \text {where } \left[ \mathrm { H } ^ { + } \right]$ is the concentration of hydrogen ions in moles per liter in the solution. Use this formula to -The pH value of a substance is 5.42 . Find the hydrogen-ion concentration for this substance.

A dentist can sell his practice for $1,100,000 cash or for $250,000 plus $270,000 at the end of each year for 4 years. (a) Find the present value of the annuity that is offered if money is worth 8% compounded annually. (b) If She takes the $1,100,000, spends $250,000 of it, and invests the rest in a 4-year annuity at 8% compounded Annually, what size annuity payment will she receive at the end of each year? (c) Which is better, taking the $250,000 and the annuity or taking the cash settlement?

Evaluate the function. Round to two decimal places. -Evaluate $\frac { 64 } { 1 + 0.2 e ^ { - 0.06 x } } \text { when } x = 18$

Rewrite the expression as the sum and/or difference of logarithms, without using exponents. Simplify if possible. - $\log _ { 17 } \frac { 5 \sqrt { x } } { y }$

Use a change of base formula to evaluate the given logarithm. Approximate to three decimal places. - $\log _ { 5 } ( x + 7 ) + \log _ { 5 } ( x - 7 ) = 1$

A company predicts that sales will increase rapidly after a new product is released, with the number of units sold weekly modeled by N $\mathrm { N } = 3000 ( 0.2 ) ^ { 0.7 ^ { t } }$ , where t represents the number of weeks after the product is released. Use graphical or numerical methods to find the first week in which 2250 units were sold.

What is the range of the function $y = \left( \frac { 1 } { 5 } \right) ^ { x }$ ?