Question

A farmer buys a tractor for 50,000. If the tractor depreciates 10% per year, what is the value of the tractor in 7 years? :)))

Answer 1

$23,914.85 (nearest cent).

Explanation:

`\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}`

The given scenario can be modelled as an exponential equation.

The initial value (a) is the purchase cost of the tractor.

As the tractor depreciates by 10% each year, the value of the tractor is 90% of the previous year's value. Therefore, the base (b) is 0.9.

Therefore, the equation is:

`\boxed{y=50000(0.9)^x}`

where:

• x is time (in years).
• y is the value of the tractor (in dollars).

To find the value of the tractor in 7 years, substitute x = 7 into the equation:

`\implies y=50000(0.9)^7`

`\implies y=50000 * 0.4782969`

`\implies y=23914.845`

Therefore, the value of the tractor in 7 years is $23,914.85 (nearest cent).

Answer 2

In order to complete the equation we need to use this method :

Remaining Amount = I(1-r)^t

I=Initial Amount

R=DECAY rate

T=Time periods

(Exponential Decay btw if you didnt know is when a population or group of something is declining, and the amount that decreases is proportional to the size of the population)

Now that we know that Time for Some Exponential Decay fun :D *sarcasm* :p

The farmer purchased a tractor for 50,000 so you start with that:

Remaining Amount = 50,000(1-r)^t

Decay rate would be 0.10 because you have to CONVERT 10% to decimal form.

Remaining Amount = 50,000(1-0.10)^t

Now time period would be 7 of course:

Remaining Amount = 50,000(1-0.10)^7

TIME TO SOLVE:

Answer 23914.845 BUT you have to round to nearest cent so then the answer would be:

23914.85

Explanation:

I learned this in my math class. ~Good------Night