Question

woich statement(s) can be interpreted from the equation for an automobile cost, c(t)=28,000(0.7)
And t represents the time in years?
Select all correct statements.
A $28,000 represents the initial cost of an automobile that appreciates 73% per year over the cor
8. The equation is an exponential decay equation.
c. $28,000 represents the initial cost of an automobile that depreciates 73% per year over the cou
D. $28,000 represents the initi& Zost of an automobile that appreciates 27% per year over the cou​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

An automobile cost C(t) and time in years, t, is represented by C(t) = 28,000(0.73)t.

• $28,000 is the initial cost of an automobile that depreciates 27% per year.

• $28,000 is the initial cost of an automobile that depreciates 73% per year.

• $28,000 is the initial cost of an automobile that appreciates 73% per year.

EVALUATION

Here it is given that the automobile cost C(t) and time in years, t, is represented by

$\displaystyle \sf{C(t) = 28000 \times {(0.73)}^{t} }$

Which can be rewritten as

$\displaystyle \sf{C(t) = 28000 \times { \bigg( \frac{73}{100} \bigg)}^{t} }$

$\displaystyle \sf{ \implies \: C(t) = 28000 \times { \bigg( 1 - \frac{27}{100} \bigg)}^{t} }$

From above we see that

The initial cost of an automobile = $28,000

The rate at which it depreciates = 27% per year.

FINAL ANSWER

Hence the correct option is

$28,000 is the initial cost of an automobile that depreciates 27% per year.

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Answer 2

Given : c(t)=28,000(0.73)^t

To Find : which statement(s) can be interpreted from the equation

A $28,000 represents the initial cost of an automobile that appreciates 73% per year  

B). The equation is an exponential decay equation.

c). $28,000 represents the initial cost of an automobile that depreciates 73% per year  

D. $28,000 represents the initial & Cost of an automobile that appreciates 27% per year  

Solution:

c(t)=28,000(0.73)^t

t = 0

=> Cost = 28,000(0.73)⁰  = 28000 * 1  = 28000

Hence initial cost is 28000

t = 1

=>  Cost = 28,000(0.73)¹  = 28000 * 0.73  = 28000 * (1 - 0.27)

= 28000 - 28000(0.27)

= 28000 - 27 % of 28000

Hence depreciates 23% per year

The equation is an exponential decay equation.

$28,000 represents the initial cost of an automobile that depreciates 23% per year over

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