Question

The expression 5(2)' gives the number of leaves in a plant as a function of the number of weeks since it

was planted.
Exponentia
What does 2 represent in this expression?
A: the plant was planted 2 weeks ago
B: there were initially 2 leaves in the plant
C: the number of leaves is multiplied by 2 each week

Answer 1

C: the number of leaves is multiplied by 2 each week

Explanation:

The right expression should be 5(2) ^ t =
`5(2)^(t)`

where t represent the number weeks after it planted.

If we put 0 to the time(t) we will know how many leaves initially are. The calculation will be:

`5(2)^(t)`=
`5(2)^(0)` =5

This show that coefficient 5 determine how much the leaves initially are.

Let see how the number going for different value of t. If its 1 week after plant, the leaf will become:

`5(2)^(t)`=
`5(2)^(1)` = 10

Then the number of leaves 2 weeks after planted will be:

`5(2)^(t)`=
`5(2)^(2)`= 20

The number keeps double every week since coefficient 2 represents the ratio of the growth of the function and the ratio determines how much leaves multiplied each week.

So, the answer will be C.