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

Option (D) is correct.

Step-by-step 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

Now, map our problem using the same concept formula

as

3000 students were enrolled, so

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

so substituting b = 0.022 and a = 3000

y = a (1-b)ˣ

y = 3000 (1 - 0.022)ˣ

as

so the expression becomes

y = 3000 (0.978)ˣ

Therefore, option (D) is correct.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).