Hello, Lissa,
a. Write an equation to find the value, y, of the car, x years after it was purchased.
y = 8000*(1.05)x [The (1.05) represents the value increased by 5%, and the exponent repeats that for x years).
b. If you wanted to graph your equation from part (a), what would be the y-intercept?
8000, the value at time = 0, when the car was purchased
c. Explain what the y-intercept represents in context.
See answer above. The initial value of the car, at time = 0
d. Will the value of the car ever be lower than $8,000?
Not enough information provided to give a positive answer. The equation says no, but we can't promise the 5% growth will continue forever.
e. Explain your reasoning for your answer from letter d.
The 5% increase is based on assumptions that are unlikely to persist long term. My crystal ball broke down during the last financial crisis.
f. Using your answer from part c, write an inequality to describe the range.
y = 8000*(1.05)x for 0<x<20 (Put whatever maximum years you feel comfortable promising the 5% growth rate). I assume the assumptions are reasonable for 20 years, but I also bought Enron stock, so you are on your own here.
g. If Marvin plans to sell his car in the future to make a profit, how much more money will he make if he sells the car in 10 years than if he sells it in 5 years?
5 year value = 8000*(1.05)5 = 10210
10 year value = 8000*(1.05)10 = 13031
Difference = $2821 additional value
I hope this helps, and makes sense,
Bob
