Question

An ant population starts at 1200 for a certain colony. As each month goes by in the winter, 6.5% of the population dies off. How many of the ants should be alive after 4 months? (Round to the whole ant.)

Answer 1

Answer: 917 ants should be alive after 4 months.

Step-by-step explanation:

As each month goes by in the winter, 6.5% of the population dies off. It means that the population is decaying exponentially. We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the population after t months.

t represents the number of months.

P represents the initial population.

r represents rate of decay.

From the information given,

P = 1200

r = 6.5% = 6.5/100 = 0.065

t = 4 months

Therefore,

A = 1200(1 - 0.065)^4

A = 1200(0.935)^4

A = 917

Answer 2

Answer:

There will be 916 ants alive after 4 months.

Step-by-step explanation:

Step 1

Let's change the percentage to a decimal by dividing by a 100.

6.5% / 100 = .065

Step 2

So, for the first month we will multiply the initial amount of ants by .065 and this will give us the number of ants that die.

1200 * .065 = 78

This means that after the first month, 1200 - 78 = 1122 ants will be alive.

Step 3

Now for the second month: 1122 * .065 = 72.93 (rounded to 73)

1122 - 73 = 1049 ants will be alive

Step 4

For the third month 1049 * .065 = 68.185 (rounded to 68)

1049 - 68 = 981 ants will be alive

Step 5

For the fourth month 981 * .065 = 63.765 (rounded to 64)

981 - 64 = 916 ants will be alive

Hope this helps!