Respuesta :

roohafzah

Answer :

  • $9396

Explanation :

to find the value of the car at the end of the 4th year,we can use the formula for exponential decay which is given by,

  • y = a(1 - b)^x

where,

  • y = value over the time period 'x'.
  • x = time period
  • a = original value
  • b = rate of decay

plugging in,

  • y = $18000(1-0.15)^4
  • y = $9396.1125

thus, by the end of the 4th year, the car will be worth nearly $9396 .

______

the depreciation rate is 15% per year i.e. the car's value would become 85% of it's original value

value of the car after 1 year

  • $18000*0.85 = $15300

value of the car after 2 years

  • $15300*0.85 = $13005

value of the car after 3 years

  • $13005*0.85 = $11054.25

value of the car after 4 years

  • $11054.25*85 = $9396 ( to the nearest $ )

thus,the value of the car at the end of the 4th year will be equal to $9396.

semsee45

Answer:

$9,396

Step-by-step explanation:

Jane bought a new car for $18,000. To find the value of the car at the end of 4 years after depreciating by 15% each year, we can use the formula for exponential decay:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Exponential Decay}}\\\\A=P(1-r)^{t}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$A$ is the final value.}\\\phantom{ww}\bullet\;\textsf{$P$ is the initial value.}\\\phantom{ww}\bullet\;\textsf{$r$ is the rate of decay (in decimal form).}\\\phantom{ww}\bullet\;\textsf{$t$ is the time (in years).}\end{array}}[/tex]

In this case:

  • P = $18,000
  • r = 15% = 0.15
  • t = 4 years

Substitute the values into the formula and solve for A:

[tex]A=18000(1-0.15)^4\\\\A=18000(0.85)^4\\\\A=18000(0.52200625)\\\\A=9396.1125\\\\A=\$9396\; \sf (nearest\;dollar)[/tex]

So, the value of the car at the end of 4 years rounded to the nearest dollar is:

[tex]\LARGE\boxed{\boxed{\sf \$9,396 }}[/tex]

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