Question

In 2019-2020, North Carolina spent $10,632 per student. The per-pupil spending has decreased at 6% per year. If this continues, what will be the per-pupil spending in 4 years?

Answer 1

The per-pupil spending will be approximate $8,300 in 4 years

Explanation:

Exponential Model

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the current quantity.

An exponential decaying function is expressed as:

`C(t)=C_o\cdot(1-r)^t`

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The statistics of the years 2019-2020 at North Carolina indicate initial spending of Co=10,632 per student. The decaying rate is r=6% = 0.06 per year, thus the exponential model is:

`C(t)=10,632\cdot(1-0.06)^t`

`C(t)=10,632\cdot(0.94)^t`

where t is expressed in years.

We are required to know the expected spending for t= 4 years. Substitute t=4:

`C(t)=10,632\cdot(0.94)^4\approx 8,300`

The per-pupil spending will be approximate $8,300 in 4 years