Question

Dakota found a vintage skateboard from the 1980s in her parents' garage. The owner of the local skate shop told her the skateboard is currently worth $380 and will increase in value by about 7% each year.

Write an exponential equation in the form y=a(b)x that can model the skateboard's value, y, in x years.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =
To the nearest dollar, how much will the skateboard be worth in 7 years?
$

Answer 1

The skateboard's value can be modeled by the exponential equation y = 380(1.07)^x, where x is the number of years. To find its value in 7 years, we calculate y ≈ 624, so the skateboard will be worth approximately $624.

Step-by-step explanation:

To model the skateboard's value, we need an exponential equation that reflects its initial value and its percent increase each year. The initial value is the current worth of the skateboard, which is $380, and it increases at a rate of 7% each year.

The general form of an exponential function is y = a(b)^x, where a is the initial amount, b is the growth factor, and x represents time (in this case, years).

Since the skateboard's value increases by 7% each year, the growth factor, b, is 1 plus the percent increase written as a decimal, so b = 1.07. Therefore, the exponential equation representing the skateboard's value in x years is:

y = 380(1.07)^x

To determine the value of the skateboard in 7 years, we would substitute x with 7:

y = 380(1.07)^7

We then calculate this value to find out how much the skateboard will be worth, rounding to the nearest dollar.

Using a calculator, we get y ≈ 380(1.642) ≈ $624.36. Therefore, to the nearest dollar, the skateboard will be worth approximately $624 in 7 years.