Question

Kylie recorded the number of pears on a pear tree at the end of every week. The following function represents the number of pears on the pear tree, where x represents the number of weeks.

P(x) = 2^(2 + x)

Which statement is true?

The number of pears on the tree quadruples each week.

The number of pears on the tree increases by 2 each week.

The number of pears on the tree increases by 4 each week.

The number of pears on the tree doubles each week.

Answer 1

nvmd i see that it would be D


First, use the properties of exponents to rewrite the function.

P(x) = 2^(2 + x)
= 2^2 • 2^x
= 4 • 2^x
= 4(1 + 1)^x

In the expression, 4(1 + 1)x, four is the initial number of pears on the tree, and (1 + 1)x reveals the rate of increase (100%) of the number of pears on the tree.

Therefore, the number of pears on the tree doubles each week.