Question

The function f describes the value of a sculpture after t years. The function g describes the value of a painting by the same artist after t years.

f(t) = 500(1.2)^t
g(t) = 380(1.15)^t

Find function h, such that h(t) = f(t) - g(t).

h(x) = 120(1.05)^t
h(t) = 880(1.35)^t
h(t) = 20[25(1.2)^t - 19(1.15)^t]
h(t) = 20[19(1.2)^t - 25(1.15^t]

Answer 1

h(t)=ft)-g(t)
h(t)=500(1.2)^t-380(1.15)^t
Getting out 20 common factor:
h(t)=20[500(1.2)^t/20-380(1.15)^t/20]
h(t)=20[25(1.2)^t-19(1.15)^t]
Answer: Third option: h(t)=20[25(1.2)^t-19(1.15)^t]

Answer 2

h(t) = f(t) - g(t)
= 500(1.2)^t - 380(1.15)^t
Taking out the greatest common factor, which is 20:
= 20[(25)(1.2)^t - (19)(1.15)^t]
This is the third choice.

Note that you cannot subtract the bases of the exponents, for example (1.2^t - 1.15^t) cannot be simplified into something like 0.05^t.