Question

How do the average rates of change for the pair of functions compare over the given interval?

f(x)=0.9x^2
g(x)=2.7x^2

1≤x≤5

The average rate of change of f(x) over 1 ≤x≤5 is ☐.The average rate of change of g(x) over 1≤x≤5 is ☐.The average rate of change of g(x) is ☐ times that of f(x)

-(Simplify your answers. Type integers or decimals.)

Answer 1

To compare the average rates of change for the pair of functions, you need to find the average rate of change of each function over the given interval.

Step-by-step explanation:

To compare the average rates of change for the pair of functions, we need to find the average rate of change of each function over the given interval.

For the function f(x) = 0.9x^2, the formula for average rate of change is:

Average Rate of Change = (f(b) - f(a))/(b - a)

Substituting the values for a = 1 and b = 5:

Average Rate of Change for f(x) = (f(5) - f(1))/(5 - 1) = (0.9(5^2) - 0.9(1^2))/(5 - 1) = (22.5 - 0.9)/(4) ≈ 5.15

Similarly, for the function g(x) = 2.7x^2, the average rate of change can be calculated as:

Average Rate of Change for g(x) = (g(5) - g(1))/(5 - 1) = (2.7(5^2) - 2.7(1^2))/(5 - 1) = (67.5 - 2.7)/(4) ≈ 16.45

Answer 2

9514 1404 393

Answer:

3 times

Step-by-step explanation:

We observe that both functions are vertically scaled versions of the parent quadratic y = x^2. The ratio of scale factors is 2.7/0.9 = 3. That is, ...

g(x) = 3f(x)

This means that whatever vertical difference f(x) may show over the interval, g(x) will show 3 times that difference.

The average rate of change of g(x) is 3 times that of f(x).