Question

A farmer is monitoring the water content of the soil during a dry summer. The water content of the soil is decreasing at a rate of 2.5% per

week. If a certain soil sample contains 200 grams of water on July 1st, which equation describes the relationship between y, amount of

water in grams, and t, time in weeks after July 1st?

• A. y=200(0.75)'

B. y=200(0.975)

•

C. y=200 - 0.025

D. y = 200 - 0.25t

Answer 1

`y=200(0.975)^t`

Explanation:

The general exponential growth or decay function is

`y=a(1+r)^t` .... (1)

where, a is initial value, r is rate of change and t is time.

From the given information it is clear that

Initial water content of the soil = 200 grams

The water content of the soil is decreasing at a rate of 2.5% per.

Rate of change = -0.025

Substitute these values in equation (1).

`y=200(1+(-0.025))^t`

`y=200(1-0.025)^t`

`y=200(0.975)^t`

Therefore, the required equation is
`y=200(0.975)^t`.