Question

Tom is 77 inches tall and shrinking at a rate of 0.75% every eyar. How tall will he be after 15 years?

Whats the exponential function

Answer 1

The exponential funtion is "height(n) = 77*(0.9925)^n". After 15 years he is 68.7778 inches.

Explanation:

Since Tom's initial height is 77 inches. After one year:

height(1) = 77*(1 - 0.0075) = 77*0.9925

After two years:

height(2) = height(1)*(0.9925) = 77*0.9925*(0.9925) = 77*(0.9925)²

After three years:

height(3) = height(2)*0.9925 = 77*(0.9925)²*0.9925 = 77*(0.9925)³

And so on, therefore the expression that represents his height is:

height(n) = 77*(0.9925)^n

Where n is the number of elapsed years. For 15 years we have:

height(15) = 77*(0.9925)^(15) = 68.7778 inches

The exponential funtion is "height(n) = 77*(0.9925)^n". After 15 years he is 68.7778 inches.