What is the difference in the graph when a
whole number is raised to the exponent vs
when a fraction is raised to the exponent.

In order to understand exponential equations with a whole number and a fraction, we have to revisit the definition.

Exponentiation is just repeated multiplication. For instance, if we have 2^3, we can see that 2 * 2 * 2 = 8. The number keeps getting bigger.

Likewise, if we have (1/2)^3, 1/2 * 1/2 * 1/2 = 1/8. The number keeps getting smaller. Notice a pattern?

When we have a number greater than 1 as a base in an exponential function, the number keeps growing. This is called exponential growth.

In contrast, whenever we have a number less than 1 as a base (i.e. a fraction), the number keeps getting smaller. This is called exponential decay.

Hope this helps.

1e+27

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40