Question

A corn field has an area of 80,000 square feet. A new parasite has caused the area of the corn field to decrease by one-fourth each month. Which equation can be solved to determine the number of months, t, when the area of the corn field is 33,750 square feet, and how long will it take?

Answer 1

A. 33750 = 80000×
`((3)/(4))^(t)`

B. time taken = 3 months

Explanation:

Area of the corn field is 80000 square feet. A new parasite decreases the size of corn field by one fourth every month.

After one month remaining area of the corn field =
`1-(1)/(4)=(3)/(4)` area of the field.

Area decreases exponentially every month so the decrease after time t will be = (total area)×(
`((3)/(4))^(t)`

= (80000)×(
`((3)/(4))^(t)`

This decrease in time t is equal to 33750 feet².

Therefore the equation will be 33750 = 80000×
`((3)/(4))^(t)`

By solving this equation we can find the time taken.

By taking log on both sides

`log(33750)=log(80000)((3)/(4))^(t)`

4.528 = log(80000) + tlog(0.75)

4.528 = 4.903 + t(-0.125)

4.528 - 4.903 = -t(0.125)

-0.375 = -(0.125)t

t =
`(0.375)/(0.125)=3`

Therefore it will take 3 months.

Answer 2

1/4 = 25% so the field would be 75% as much each month

the equation would be something like: 80000*0.75^x
You didn't list the choices....

solve for time: 33750 = 80000*0.75^t
0.4219 = 0.75^t

t = log(0.4219) / log(0.75)
time = 3 months