Ramon had his heart set on owning his dads new car which cost $75 000, but he only had $5 000. His dad told him to put the money in the bank to earn interest, and one day, he will be able to buy the car. The dad agreed to the following model for the price of the car, t years from today ...

aluecar(t)=v0e^-0.10t

Ramon invested the money into the bank who gave him a brochure to read that said that if he withdrew his money in t years from today he would have an amount ...

avings() = 0 1.03^2 (a) Explain both modelling equations and interpret the -0.10,0 ,the1.03 and 0.

(b) Ramons dad promised to help pay for the car by promising to contribute equally to what Ramon pays when the time came. Solve for t to find how long Ramon must wait to buy his fathers car.

(Answer to the nearest month, assuming 12 equal months to the year).