Question

Zelda has 8 rabbits with which to start an animal farm. If the rabbit population doubles each month, in how many months will the rabbit population be 5,800? 1) Write the exponential equation in function notation: f x( ) = 2) Write the exponential equation in y = notation: f(x)

State the quantity the variable x represents:

State the quantity the variable y represents:

3) Solve the equation in Step 2 for x :

Rewrite the simplified equation in logarithmic function form:

g x( ) =

State the quantity the independent variable (x) represents:

State the quantity the dependent variable( y,or g(x) ), represents:

Answer 1

9.5 months

Explanation:

We would be using the expression

y = abⁿ

Where

a = starting number = 8 rabbits

b = rate of change = the number of rabbits doubles = 2

n = number of time intervals that has passed = unknown = number of months

y = rabbit population = 5800

y = abⁿ

5800 = 8 × 2ⁿ

Divide both sides by 8

5800 ÷ 8 = 2ⁿ

725 = 2ⁿ

n = 9.5 months.

Therefore, the number of months in which the rabbit population would reach 5,800 is 9.5 months