Question

Read the problem to choose the correct method, then solve. A farmer buys a tractor for $50,000. If the tractor depreciates 10% per year, use an exponential function to find the value of the tractor in 7 years. AD CO Exponential Growth, $97,435.86 Exponential Decay, $23,914.85 Exponential Growth, $315,000 Exponential Decay, 21,523.36​

Answer 1

The correct option is, Exponential Decay, $23,914.85.

Explanation:

A farmer buys a tractor for $50,000.

It is provided that the the tractor depreciates 10% per year.

The exponential function for decay is:

`y=a\cdot (1-r\%)^(t)`

Here,

a = initial value

r = decay rate

t = time

Compute the value of the tractor in 7 years as follows:

`y=a\cdot (1-r\%)^(t)`

`=50000* (1-0.10)^(7)\\\\=50000* 0.4782969\\\\=23914.845\\\\\approx 23914.85`

Thus, the correct option is, Exponential Decay, $23,914.85.