Question

The function H(t)=260,000(1.038)^t represents the value of a house t years after it was purchased.
Complete the sentence.
The house's value is increasing at a rate of
% each year, and its purchase price was $
.

Answer 1

To complete the sentence, we need to determine the annual growth rate and the purchase price of the house from the given function \( H(t) = 260,000(1.038)^t \).

1. **Annual Growth Rate**: The function is of the form \( H(t) = P(1 + r)^t \), where \( P \) is the initial value (purchase price) and \( r \) is the growth rate.

In this case, \( r = 0.038 \) or \( 3.8\% \).

2. **Purchase Price**: From the function, the purchase price is represented by the constant in front of the exponential term, which is \( 260,000 \).

Now, we can fill in the blanks:

The house's value is increasing at a rate of **3.8%** each year, and its purchase price was **$260,000**.