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?
A.
The number of pears on the tree quadruples each week.

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

C.
The number of pears on the tree doubles each week.

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

Answer 1

To analyze the function \( P(x) = 2(2 + x) \), we can simplify it:

\[
P(x) = 2 \cdot 2 + 2 \cdot x = 4 + 2x
\]

Now, let’s find the change in the number of pears from week to week. We can find \( P(x) \) and \( P(x + 1) \):

\[
P(x) = 4 + 2x
\]

\[
P(x + 1) = 4 + 2(x + 1) = 4 + 2x + 2 = 6 + 2x
\]

Now we can find the increase in the number of pears from week \( x \) to \( x + 1 \):

\[
P(x + 1) - P(x) = (6 + 2x) - (4 + 2x) = 6 + 2x - 4 - 2x = 2
\]

This calculation shows that the number of pears increases by 2 each week.

Thus, the correct statement is:

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