determine the function.

Question

The profit of Spacely’s SprocketsTM at time t is calculated by the function 𝑃(𝑡) = 156(3𝑡 + 2)^1/ 2, where P is measured in millions of dollar. The Number of sprockets in production is calculated by 𝑁(𝑡) = 4(3𝑡 + 2)^1/9. Determine a function for the profit per sprocket S(t) by finding ( 𝑃 𝑁 ) (𝑡). Simplify your answer.

Answer 1

[156(3t + 2)^1/2]/[4(3t + 2)^1/9] = (156/4)(3t + 2)^{1/2 - 1/9}

1/2 - 1/9 = 9/18 - 2/18 = 7/18

S(t) = 39(3t + 2)^7/18