Question

The exponential function k(x) increases at a rate of 75% through the ordered pair (0, 8) and approaches a horizontal asymptote at y = 2. Use a graph of the function to determine the range.

A. (7, ∞)
B. (-∞, 7)
C. (2, ∞)
D. (-∞, 2)

Answer 1

B. (-∞, 7)

Explanation:

It increases at a rate of 75%, which means the base of the exponential function is 1 + 0.75 = 1.75.

It passes through the ordered pair (0, 8), which means k(0) = 8.

It approaches a horizontal asymptote at y = 2, which means as x approaches positive or negative infinity, the function approaches y = 2.

We can write the exponential function as:

k(x) = 8 * (1.75)^x

Now, let's consider the range. As x increases to positive infinity, the function k(x) will also increase without bound. Therefore, the range of the function is: B. (-∞, 7)