Question

Ms. Clark bought a house. The value of the house appreciated at a constant rate per year. If she bought the house for $250,000 and a year later it was valued at $267,500. What function can be used to find the value of her house after t years.

f(x) = 250,000(1.07)ᵗ
f(x) = 267,500(0.07)ᵗ
f(x) = 250,000(0.07)ᵗ
f(x) = 267,500(1.07)ᵗ

Answer 1

The function that represents the value of Ms. Clark's house after t years, accounting for a 7% annual appreciation, is f(x) = 250,000(1.07)^t.

Step-by-step explanation:

The value of Ms. Clark's house appreciated from $250,000 to $267,500 in one year. This represents a 7% increase because $267,500 is 107% of $250,000. Therefore, the function that can be used to find the value of her house after t years is f(x) = 250,000(1.07)t. This represents the initial value of the house multiplied by 1.07 (the 7% appreciation) raised to the power of t, the number of years.

Neither of the other functions listed correctly represents the situation described, as they either use the incorrect initial value, the incorrect rate, or do not raise the rate to the power of t. Thus, the correct function is f(x) = 250,000(1.07)t.