8) This exercise uses the radioactive decay model. The half-life of strontium-90 is 28 years. How long will it take a 70-mg sample to decay to a mass of 53.2 mg? (Round your answer to the nearest whole number.)

9) Evaluate the expression. (Simplify your answer completely.)

(a)

log₄(0.125)

10) Consider the following.

5e^x = 26

(a) Find the exact solution of the exponential equation in terms of logarithms.

x = (b) Use a calculator to find an approximation to the solution rounded to six decimal places.

x =

12) Solve the logarithmic equation for x, as in Example 7. (Enter your answers as a comma-separated list.)

log(x) + log(x 1) = log(3x)

x =

13) Use the Laws of Logarithms to evaluate the expression.

log₅(25²⁰⁰)

14) Evaluate the expression. (Simplify your answer completely.)

(c) log₉(9¹²)

16) Vilfredo Pareto (1848-1923) observed that most of the wealth of a country is owned by a few members of the population. Pareto's Principle islog(P) = log(c) k log(W)where W is the wealth level (how much money a person has) and P is the number of people in the population having that much money.(a) Solve the equation for P.

P =

(b) Assume k = 1.7, c = 9000, and W is measured in millions of dollars. Use part (a) to find the number of people who have $2 million or more. (Round your answer to the nearest whole number.) people? How many people have $10 million or more? (Round your answer to the nearest whole number.) people?

18) Animal populations are not capable of unrestricted growth because of limited habitat and food supplies. Under such conditions the population follows a logistic growth model:

P(t) =

d

1 + ke^ct

where c, d, and k are positive constants. For a certain fish population in a small pond d = 1000, k = 9, c = 0.2, and t is measured in years. The fish were introduced into the pond at time t = 0.(a) How many fish were originally put in the pond? fish (b) Find the population after 10, 20, and 30 years. (Round your answers to the nearest whole number.)

10 years	fish
20 years	fish
30 years	fish

(c) Evaluate P(t) for large values of t. What value does the population approach as t? P(t) =

22) A certain breed of mouse was introduced onto a small island with an initial population of 260 mice, and scientists estimate that the mouse population is doubling every year.(a) Find a function N that models the number of mice after t years.

N(t) =

260 2t

(b) Estimate the mouse population after 7 years. mice