A. The decrease in Car 1 value is constant at 6000 from year to year. Its value can be described by a linear function.
The decrease in Car 2 value is a constant percentage of its current value from year to year. Its value can be described by an exponential function.
B. The slope of the Car 1 function is -6000, and the value is 32000 in year 1, so the value function for Car 1 can be written as
... f(x) = 32000 -6000(x-1)
... f(x) = 38000 -6000x
The value multiplier for Car 2 from year to year is 27455/32300 = 0.85, so the value function for Car 2 can be written as
... f(x) = 32,300·0.85^(x-1)
... f(x) = 38000·0.85^x
C. There is a significant difference in value after 5 years. Car 2 is worth more than double the value of Car 1 in year 5. That year, their values are ...
... car 1: $8000
... car 2: $16861
Let's call the store value as s and the wholesale price as w. A store prices tapes by raising the wholesale price 50%(0.5 in decimals) and adding 25 cents, writing this as an equation, we have
If we invert the equation we're going to find the the wholesale price as a function of the store price.
Now, to find the wholesale price if the sales price is $1.99, we just need to evaluate s = 1.99 on the function we created.
The wholesale price is $1.16.