Question

Exponential function f is represented by the table. Function g is an exponential function passing through the points (0,27) and (3,0). Which statement correctly compares the behavior of the two functions on the interval (0, 3)?

A) Both functions increase on the interval.
B) Function g increases, while function f decreases.
C) Function f increases, while function g decreases.
D) Both functions decrease on the interval

Answer 1

The correct statement that compares the behavior of the two exponential functions on the interval (0, 3) is that both functions decrease on the interval.

Step-by-step explanation:

The correct statement that compares the behavior of the two exponential functions on the interval (0, 3) is option D) Both functions decrease on the interval.

Given that function g is an exponential function passing through the points (0, 27) and (3, 0), we can find the equation of g using the exponential decay formula:

g(x) = a * e-kx,

where a is the initial value (27), x is the independent variable (time), and k is the decay constant to be determined.

Substituting the given points into the equation, we get:

27 = a * e-k*0,

0 = a * e-k*3.

Solving these equations, we find that:

k = -ln(3)/3

Substituting the decay constant into the equation for g, we get:

g(x) = 27 * e-ln(3)/3 * x.

For function f, we are given a table. Based on the table, we can see that as x increases from 0 to 3, the corresponding values of f(x) decrease. Therefore, both functions g and f decrease on the interval (0, 3).