The value of Sara's new car decreases at a rate of 8% each year

1. write an exponential function to model the decrease in the car's value each month.
2. write an exponential function to model the decrease in the car's value each week.
3. write an exponential function to model the decrease in the car's value each day.
4. what relationship is there between the amount of decrease and the time interval measured

Let y be the price of the car and x be the number of years. The yearly price decrease:
y = 0.08ˣ
1) y = 0.08^(x/12)
2) y = 0.08^(x/52)
3) y = 0.08^(x/365)
4) The smaller the smaller the time interval measured, the less the amount decreases.

Answer Link

MsEHolt MsEHolt · Answer 2 · 2018-08-16T22:42:32+02:00

The correct answers are:

#1) y=(0.08/12)ˣ = 0.0067ˣ

#2) y=(0.08/52)ˣ = 0.0015ˣ

#3) y=(0.08/365.25)ˣ = 0.0002ˣ

#4) As the number for the time interval increases (more weeks than months per year, more days than weeks per year), the amount of decrease in value of the car decreases inversely.

Explanation:

The formula for the amount of decrease in the car is y=(r/n)ˣ, where r is the percent (written as a decimal) of decrease per year and n is the number of time periods per year.

For months, there are 12 months per year, so n = 12. The rate is 8%; 8% = 8/100 = 0.08. This gives us y=(0.08/12)ˣ. Dividing, we get y=(0.0067)ˣ.

For weeks, there are 52 weeks per year, so n = 52. The rate is still 0.08; this gives us y=(0.08/52)ˣ. Dividing, we get y=(0.0015)ˣ.

For days, there are 365.25 days per year, so n = 365.25. The rate is still 0.08; this gives us y=(0.08/365.25)ˣ. Dividing, we get y=(0.0002)ˣ.

Comparing the number of weeks to the number of months, 52/12 = 4.3. There are 4.3 times more weeks in a year than there are days. The amount of decrease from months to weeks went from 0.0067ˣ to 0.0015ˣ; 0.0015/0.0067 = 0.2234, which is close to 1/4.3.

Comparing the number of days to the number of weeks, 365.25/52 = 7.02. There are 7.02 times more days in a year than there are weeks. The amount of decrease from weeks to days went from 0.0015ˣ to 0.0002ˣ/ 0.0002/0.0015 = 0.1333, which is close to 1/7.02.