Question

Sara's new car depreciates 8% each year.

Write an exponential function to model the depreciation each month.
Write an exponential function to model the depreciation each week.
Write an exponential function to model the depreciation each day.
What relationship is there between the amount of depreciation and the time interval measured?

Answer 1

Wait this is all one question?

Answer 2

Yes, I need to make 3 exponential functions, 1 to show the depreciation for each month, week, and day. Then based on the results of those 3 functions, I need to find the relationship between the amount ofdepreciation and time intervals measured.

Answer 3

\[A=P(1-0.08)^t=P \left( 0.92 \right)^t per~year.\]
\[A=P \left( 1-\frac{ 8 }{100 \times 12 } \right)^{12t}=P \left( \frac{ 298 }{ 300 } \right)^{12t} ~per ~month\]

Answer 4

similarly for week
write 52 in place of 12 in place of 12 both in parenthesis and power.
and for each day write 365 in place of 12 both in parenthesis and power

Answer 5

Wait, which one is the actual function though? Or is the first one a simplified variant of the second?

Answer 6

P=present price.
A=amount after a year,week or after 1 day

Answer 7

first one simplified per year.
second one simplified per month.