Question

[HELP!! Giving 50 POINTS]A tree frog population doubles each month. Suppose that currently, there are 12 tree frogs in your backyard. Your tree can hold at most 24576 tree frogs.

What is the equation?
How many months does it take for your tree to be completely filled?

Answer 1

y = 12 *(2^x)x= 11months

Explanation:

This is exponential growth y= ab^xwhere a is the initial value (12)and b is the growth rate (doubles = 2)y =12 * 2^xWe need to know when the tree is completely filled24576 = 12 * 2^xDivide each side by 1224576/12 = 12/12 * 2^x2048 = 2^xRewriting 2048 in terms of powers of 22^11 =20482^11 = 2^xSince the bases are the same, the powers are the samex=11

Answer 2

y = 12 *(2^x)

x=11 months

Explanation:

This is exponential growth

y= ab^x

where a is the initial value (12)

and b is the growth rate (doubles = 2)

y =12 * 2^x

We need to know when the tree is completely filled

24576 = 12 * 2^x

Divide each side by 12

24576/12 = 12/12 * 2^x

2048 = 2^x

Rewriting 2048 in terms of powers of 2

2^11 =2048

2^11 = 2^x

Since the bases are the same, the powers are the same

x=11