A new car cost $18,000 to build in 2020. The company's financial analysts expect costs to rise by 6% per year. The cost to build the car can be modeled by the function f(t) = 15000 × (1.06)t
, where t is the number of years after 2020. How much did the financial analyst expect the car to cost to build in 2021? 2022? 2023? You must show all your work and calculate the cost to build the car for all 3 years in order to receive full points.(6 points)
To find the cost to build the car in 2021, we need to substitute t = 1 into the function:
f(1) = 15000 × (1.06)^1
= 15000 × 1.06
= $15,900
So, the financial analyst expected the car to cost $15,900 to build in 2021.
To find the cost to build the car in 2022, we need to substitute t = 2 into the function:
f(2) = 15000 × (1.06)^2
= 15000 × 1.1236
= $16,854
So, the financial analyst expected the car to cost $16,854 to build in 2022.
To find the cost to build the car in 2023, we need to substitute t = 3 into the function:
f(3) = 15000 × (1.06)^3
= 15000 × 1.191016
= $17,865.24
So, the financial analyst expected the car to cost $17,865.24 to build in 2023.