Question

A house is purchased for $200,000 and its value appreciates by 2.75% every 3 years. Write an exponential model: p(t) = a * b�����. In how many years will the house be worth $400,000?

Answer 1

To find out in how many years the house will be worth $400,000, we can set p(t) to be 400,000 and solve for t. The house will be worth $400,000 after approximately 10.77 years.

Step-by-step explanation:

To write an exponential model for the value of the house, we use the formula p(t) = a * b, where t represents the number of years, a represents the initial value of the house, and b represents the growth factor. In this case, the initial value of the house is $200,000. Since the value appreciates by 2.75% every 3 years, the growth factor is 1 + (2.75/100) = 1.0275. Therefore, the exponential model is p(t) = 200,000 * (1.0275)^t.

To find out in how many years the house will be worth $400,000, we can set p(t) to be 400,000 and solve for t. The equation becomes 400,000 = 200,000 * (1.0275)^t. Divide both sides by 200,000 and take the logarithm with base 1.0275 to solve for t. The calculation gives t ≅ 10.77. Therefore, the house will be worth $400,000 after approximately 10.77 years.