Question

The value of a car that depreciates over time can be modeled by the function:

H(t) = 14000(0.8)^t
Write an equivalent function of the form H(t) = ab^t.
a) H(t) = 14000(0.8)^t
b) H(t) = 14000(2^-0.25)^t
c) H(t) = 14000(2^0.25)^t
d) H(t) = 14000(0.2)^t

Answer 1

The equivalent function to H(t) = 14000(0.8)^t in the form of H(t) = ab^t is H(t) = 14000(2^-0.25)^t, which is option b.

Step-by-step explanation:

The question asks for an equivalent function to the model H(t) = 14000(0.8)^t in the form of H(t) = ab^t. To transform the function into the desired form, we should look for a base that could be expressed as a power of 2 that is equivalent to 0.8. The correct transformation is to recognize that 0.8 is the same as 2^(-0.25), meaning that 0.8 can be written as (2^-0.25). Therefore, the equivalent function is option b) H(t) = 14000(2^-0.25)^t.