Question

Graph a system of equations to approximate the value of x, the rate of depreciation. Give your answer as a percent. About 4% about 13% about 1. 2% cannot be determined.

Answer 1

Depreciation involves the reduction in the value of a quantity

The rate of depreciation is about 13%

How to determine the equation

From the question, we have the following ordered pairs

(x,y) = {(0,9000) and (5,4500)}

The depreciation equation is represented as:

$y = ab^x$

At (0,9000), we have:

$ab^0 = 9000$

$a = 9000$

At (5,4500), we have:

$ab^5 = 4500$

This gives

$9000b^5 = 4500$

Solve for b^5

$b^5 = 0.5$

Take the 5th roots

$b = 0.87$

So, we have:

$y = ab^x$

$y = 9000(0.87)^x$

The rate (r) is then calculated as:

$1 -r = b$

This gives

$r =1 - b$

$r =1 - 0.87$

$r =0.13$

Express as percentage

$r= 13\%$

Hence, the rate of depreciation is about 13%

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