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) explain in three to four sentences
To calculate the cost of the car in 2021, we substitute t=1 into the equation f(t) = 15000 × (1.06)^t. This gives us f(1) = 15000 × (1.06)^1 = $15,900.
For 2022, we substitute t=2 into the equation to get f(2) = 15000 × (1.06)^2 = $16,794.
Lastly, for 2023, we substitute t=3 into the equation to get f(3) = 15000 × (1.06)^3 = $17,829.
Therefore, the financial analyst expected the car to cost $15,900 in 2021, $16,794 in 2022, and $17,829 in 2023.