Question

suppose that the dollar value ( v(t) ) of a certain house that is ( t ) years old is given by the following exponential function. ( v(t) = 320,000(0.77)^t )
find the initial value of the house. ($ square)
does the function represent growth or decay? (\bigcirc) growth (\bigcirc) decay
by what percent does the value of the house change each year? (square%)

Explanation:

Step1: Find initial value (t=0)

$v(0)=320,000(0.77)^0 = 320,000(1) = 320,000$

Step2: Identify growth/decay

Base $0.77 < 1$, so it is decay.

Step3: Calculate annual percent change

$1 - 0.77 = 0.23 = 23\%$ (decrease)

Answer:

Initial value of the house: $\$320,000$
The function represents: decay
Annual percent change: $23\%$ decrease