There are 72 mice in Mouse Town. The population of mice in mouse town doubles every 8 months. How long ago was the population of mice less than ten? Make brainlest ( don't remember what's it called)

aka 24 months

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Explanation:

The population follows this function

y = 72*(2)^x

where x is the number of eight-month periods and y is the population.

So if for instance we had x = 2, then it represents two periods of 8 months each, giving 2*8 = 16 months total.

Normally with timescale problems like this, negative time values do not make sense. However, having x be negative will allow us to look back in time to figure out when y < 10.

Let's see what x is when y = 10.

y = 72*(2)^x

10 = 72*(2)^x

10/72 = 2^x

0.1389 = 2^x approximately

log(0.1389) = log(2^x)

log(0.1389) = x*log(2)

x = log(0.1389)/log(2)

x = -2.8479 also approximate

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If x = -2, then,

y = 72*(2)^x

y = 72*(2)^(-2)

y = 18

and if x = -3, then,

y = 72*(2)^x

y = 72*(2)^(-3)

y = 9

This means that 3 eight-month periods ago, the population was less than 10 mice.

So this is 3*8 = 24 months = 2 years.

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Checking the

If we were to start at 9 mice and double the population, then it goes to 18 mice. Then that doubles to 36, and so on.

Here's a table showing this process

The table confirms the answer of 24 months = 2 years.

The process of using logs is almost like reversing this process shown in the table.

75

step-by-step explanation: