One cattle farmer plans to grow his cattle population 2 percent each year, modeled by the function f of t is equal to 100 times 1 point 0 2 to the t th power Another farmer intends to add 20 cattle per year, modeled by the function g of t is equal to 100 plus 20 t For this application, the domain is restricted to t is greater than or equal to 0 . If the farmers become partners, which function represents the total cattle they will have after t years?
Answer
A
h of t is equal to 200 times 21 point 0 2 to the t th power
B
h of t is equal to 2 comma 000 t 1 point 0 2 t plus 100
C
h of t is equal to 200 times 20 point 4 to the t th power
D
h of t is equal to 100 times 1 point 0 2 to the t th power plus 20 t plus 100
Explanation
To find the partners’ total cattle, add the two farmers’ functions: f(t) + g(t) = 100(1.02)^t + (100 + 20t). Therefore, h(t) = 100(1.02)^t + 20t + 100, which is choice D.
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