Exponential Functions

Question

Identify the variables, identify the constants, write the function, solve the equation and write a complete answer.

 

Suppose the acreage of forest is decreasing by 6.5% per year because of development. If there are currently 10,500,000 acres of forest, determine the amount of forest land after 15 years.

Answer 1

"Decreasing by 6.5% per year" means decreasing to (100-6.5)%=93.5%, or .935, of the previous year's value.

After two years, the acreage will have decreased to .935² of the original value (10,500,000 acres), and after 15 years it will have decreased to .935¹⁵ of its original value, namely

.935¹⁵*10,500,000 ≈ 3,830,000 acres.

Answer 2

Dear Jenna,

 

In general, for any situation where there is exponential decay, the equation would be

 

A_t = A₀e-^kΔt

 

where A_t is the amount remaining after time Δt has passed, A₀ is the initial amount, and k is a constant, in this case 6.5% of 0.065.

 

A_t = (10,500,000 acres)*e^{(-0.065)*(15 years)} = (10,500,000 acres)*(0.377192) = 3,960,519 acres