The function H(t)=260,000(1.038)t represents the value of a house t years after it was purchased.

Question

Complete the sentence.
The house's value is increasing at a rate of
% each year, and its purchase price was $
.

Answer 1

To analyze the function \( H(t) = 260,000(1.038)^t \):

1. The yearly growth rate can be observed from the term \( 1.038 \). To find the percentage, we subtract 1 and then convert it to a percentage:

   \[ \text{Growth Rate} = (1.038 - 1) \times 100 = 0.038 \times 100 = 3.8% \]

2. The purchase price of the house is given by the constant factor in front of the exponential part, which is \( 260,000 \).

Combining this information, we complete the sentence:

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