Question

Bobby has been planting blackberries in a garden in his backyard. Bobby started with blackberries in one square foot of garden modeled by the function s(x) = 30. He is allowed to convert more of the garden, and each additional square foot he maintains allows his blackberry plants to produce more by a rate of a(x) = 1.3x-1.
Explain to Bobby how to create an equation to predict the number of blackberries he can expect based on the number of square feet he maintains. Describe how to determine the number of blackberries he will grow with 20 square feet. Use complete sentences.

Answer 1

please do not copy-paste my solution. this is just to help you formulate your response to the question.

the total # of blackberry plants in terms of x square feet is (1.3)^(x-1) as given

s(x) = 30 tells us that one square foot produces 30 blackberries

so if he wants the total # of blackberries in terms of x square feet, he simply needs to multiply the equation by 30 (as custom, put the 30 in front of the equation)

he also wants to know how many blackberries he'll grow with 20 square feet. simply plug x = 20 into the equation from the previous step and evaluate.