Question

Hopefully you can help me on this problem! I’m having a bit of trouble.

Answer 1

Since the value of the care dropped by 15% each year, then we can represent this situation by a geometric sequence with a common ratio of 100% - 15% = 85%

Change the percentage to a decimal by dividing it by 100

`\begin{gathered} a_t=a_{}((85)/(100))^(t-1) \\ a_t=a(0.85)^(t-1) \end{gathered}`

a is the initial value of the car

t is the number of years

b.

Since the initial value is $15000

Then a = 15000

The explicit formula is

`a_t=15000(0.85)^(t-1)`

c.

If t = 5

`\begin{gathered} a_5=15000(0.85)^(5-1) \\ a_5_{}=7830.09 \end{gathered}`

Then the price of the care after 5 years will be $7830.09 to the nearest cents

The value on the table is $12750

Then they are not the same

d.

If t = 7, then

`\begin{gathered} a_7=15000(0.85)^(7-1) \\ a_7=4808.66 \end{gathered}`

Then the value of the car after 7 years is $4808.66 to the nearest cent