Solve the problem.
1) The logistic growth function 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 13 months?
2) Find out how long it takes a $4175 investment to double if it is invested at 3.25% compounded semiannually. Round to the nearest tenth of a year.
3) Cindy will require $18,000 in 7 years to return to college to get an MBA degree. How much money should she ask her parents for now so that, if she invests it at 3.25% compounded continuously, she will have enough for school? (Round your answer to the nearest dollar.)
4) If Emery has $3250 to invest at 3.75% per year compounded monthly, how long will it be before he has $19500? If the compounding is continuous, how long will it be? (Round your answers to three decimal places.)
5) The function models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 700 pounds of the material are initially put into the vault, how many pounds will be left after 32 years?
6) Suppose that you have $6000 to invest. Which investment yields the greater return over 8 years: 7.15% compounded monthly or 7.15% compounded quarterly?
Solve the equation. Be sure to reject any value that is not in the domain. Give the exact answer.
7)
8) 4 ln (5x) = 16
9)
Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions.
10) 3ln (x - 4) - 2 ln x
Use Newton's Law of Cooling, , to solve the problem (bonus)
11) A lasagna removed from the oven has a temperature of 430°F. It is left sitting in a room that has a temperature of 75°F. After 6 minutes, the temperature of the lasagna is 310°F. Use Newton's Law of Cooling to find a model for the temperature of the lasagna, T, after t minutes.
lemmie92
Quiz3Summer2022.docx
0
