Question

Oakridge High School has been experiencing an annual

decline of 2.2% in enrollment since 1994. In 1994, 3000
students were enrolled. Determine the exponential
model that describes the school's enrollment over time.
y = 3000(97.8)^x
y = 3000(102.2)^x
y=3000(1.022)^x
Y= 3000(0.978)^x

Answer 1

Option (D) is correct.

Explanation:

We know that exponential decline in Math can be termed as a consistent reduction of an amount by percentage over a certain period of time.

It can be expressed using the formula

y = a (1-b)ˣ

here

• y represents the final amount

• a represents the original amount

• b represents the decay factor

• x represents the amount that has passed

Now, map our problem using the same concept formula

as

3000 students were enrolled, so

• a = 3000

as High School has been experiencing an annual decline of 2.2% in enrollment, so

• b = 2.2%= 0.022

so substituting b = 0.022 and a = 3000

y = a (1-b)ˣ

y = 3000 (1 - 0.022)ˣ

as

• 1 - 0.022 = 0.978

so the expression becomes

y = 3000 (0.978)ˣ

Therefore, option (D) is correct.