Question

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

Answer 1

A=p(1-0.08/12)^12t

A=p(1-0.08/52)^52t

A=p(1-0.08/360)^360t

0.08÷12=0.0067
0.08÷52=0.0015
0.08÷360=0.00022

Answer 2

Answer:

Since, the exponential decay function that models the present value,

$f(x)=a(1-r)^x$

Where, a shows the initial value,

r shows rate of decay per period,

x is the number of periods,

Given,

Annual rate = 8 % = 0.08

1. 1 year = 12 months

So, monthly rate, r = $\frac{0.08}{12}$

Number of periods in x years, t = 12x

Thus, the function would be,

$f(x)=a(1-\frac{0.08}{12})^{12x}$

2. 1 year = 52 weeks

So, weekly rate, r = $\frac{0.008}{52}=\frac{1}{6500}$

Number of periods in x years, t = 52x

Thus, the function would be,

$f(x)=a(1-\frac{0.08}{52})^{52x}$

3. 1 year = 365 days

So, daily rate, r = $\frac{0.008}{365}=\frac{1}{45625}$

Number of periods in x years, t = 365x

Thus, the function would be,

$f(x)=a(1-\frac{0.08}{365})^{365x}$

4. Since, with increasing time the value of car will decrease,

Hence, there is an inverse relation between the amount of decrease and the time interval measured.