Question

2) The resale value R (in dollars) of a company car after t years is estimated to be given by R(t) = 22,500(0.84)^t What is the rate of depreciation (in dollars per year) after 3 years?​

Answer 1

SOLUTION

GIVEN

The resale value R (in dollars) of a company car after t years is estimated to be given by

$\displaystyle \sf{R(t) = 22500 \times {(0.84)}^{t} }$

TO DETERMINE

The rate of depreciation after 3 years

EVALUATION

Here it is given that

The resale value R (in dollars) of a company car after t years is estimated to be given by

$\displaystyle \sf{R(t) = 22500 \times {(0.84)}^{t} }$

Which can be rewritten as

$\displaystyle \sf{R(t) = 22500 \times { \bigg( \frac{84}{100} \bigg)}^{t} }$

$\displaystyle \sf{ \implies \: R(t) = 22500 \times { \bigg(1 - \frac{16}{100} \bigg)}^{t} }$

Hence the required rate of depreciation

= 16 %

Again

$\displaystyle \sf{ \: R(3) = 22500 \times { \bigg(1 - \frac{16}{100} \bigg)}^{3} }$

$\displaystyle \sf{ \implies \: R(3) = 22500 \times 0.592704}$

$\displaystyle \sf{ \implies \: R(3) = 13335.84}$

So amount after 3 years = 13335.84

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