# Problem 827

Tony has been planting strawberries in a garden in his backyard. Tony started with strawberries in one square foot of garden modeled by the function s(x) = 20. He is allowed to convert more of the garden, and each additional square foot he maintains allows his strawberry plants to produce more by a rate of a(x) = 1.2x-1.

Explain to Tony how to create an equation to predict the number of strawberries he can expect based on the number of square feet he maintains. Describe how to determine the number of strawberries he will grow with 15 square feet. Use complete sentences.

Solution:-

function given for one square foot of garden s(x) = 20
additional square foot function a(x) = 1.2^(x-1)

equation to predict the number of strawberries is
h(x) = s(x)*a(x)
h(x) = 20(1.2 (x-1) ) ….(1)
here x denoting the number of square feet he maintain.

to find the number of strawberries he will grow with 15 square feet, we have put x = 15 in equation (1)
h(15) = 20(1.2 (15-1) )
h(15) = 20(1.2 14)
h(15) = 256.78
So there are 256 strawberries he will grow with 15 square feet.