3 years ago

Cedric and Insha solved the same equation using the calculations below.

Mathematics

1 answer:

Mariulka [41]3 years ago

3 0

The first working out is correct, z = 3

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Solution:

Given:

$V=16300(0.94)^t$

The value of a car after t - years will depreciate.

Hence, the equation given represents the value after depreciation over t-years.

To get the rate, we compare the equation with the depreciation formula.

$\begin{gathered} A=P(1-r)^t \\ \text{where;} \\ P\text{ is the original value} \\ r\text{ is the rate} \\ t\text{ is the time } \end{gathered}$

Hence,

$\begin{gathered} V=16300(0.94)^t \\ A=P(1-r)^t \\ \\ \text{Comparing both equations,} \\ P=16300 \\ 1-r=0.94 \\ 1-0.94=r \\ r=0.06 \\ To\text{ percentage,} \\ r=0.06\times100=6\text{ \%} \\ \\ \text{Hence, } \\ P\text{ is the purchase price} \\ r\text{ is the rate} \end{gathered}$

Therefore, the value of this car is decreasing at a rate of 6%. The purchase price of the car was $16,300.

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