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Question

The number of bunnies at a farm is growing according to the law of exponential growth. If there are 6 bunnies after 10 days and 36 bunnies after 30 days,how many bunnies will there be after 40 days?

Answer 1

Hi Danielle, use the equation, a_n = a₁ * (r)ⁿ, to solve your problem. You will have to use it three times.

First equation:

a₁₀ = 6

6 = a₁ * (r)¹⁰

solve for a₁:

a₁ = 6 / (r)¹⁰

Second equation:

a₃₀ = 36

36 = a₁ * (r)³⁰

Solve for a₁:

a₁ = 36 / (r)³⁰

Since a₁ from the first equation must equal a₁ from the second equation, we can equate a₁ to a₁, or,

6 / (r)¹⁰ = 36 / (r)³⁶

Cross multiply:

r³⁶ / r¹⁰ = 36 / 6

r²⁰ = 36

r = 1.0937

Knowing r, you can find a₁, using either the first or second equation:

Using the first equation, substitute for a_n, 6, and r, 1.0937:

6 = a₁ * (1.0937)¹⁰

a₁ = 6 / (1.0937)¹⁰

a₁ = 2.45

Third equation:

Substitute for a₁, 2.45, r, 1.0937, and n, 40

a₄₀ = 2.45 * (1.0937)⁴⁰

a₄₀ = 88.12

I am not sure who you get partial bunnies, but the answer, rounded, is 88.

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