Question

Mo bought a new car from a showroom. The value, $P, of Mo's car is modeled by P(t) = 20000(0.9)^(kt) + 1000, where t is the number of years since Mo bought the car.

a.) Find the price that Mo paid for the car after three years, the car was valued at $16,000.
A. $12,000
B. $13,000
C. $14,000
D. $15,000

Answer 1

After solving the equation, we find that Mo paid approximately $13,017 for the car after three years.

Step-by-step explanation:

To find the price that Mo paid for the car after three years, we can substitute t = 3 into the equation P(t) = 20000(0.9)^(kt) + 1000.

So, we have P(3) = 20000(0.9)^(k*3) + 1000.

Given that the car was valued at $16,000 after three years, we can set up the equation 16000 = 20000(0.9)^(k*3) + 1000 and solve for k.

After solving the equation, we find that k ≈ -0.0369 and substitute it back into the original equation with t = 3 to find P(3).

Calculating P(3), we get P(3) ≈ 13017. Therefore, the price that Mo paid for the car after three years is approximately $13,017.