Anest of ants initially contains 500 individuals. the population is increasing by 12% each week.

a) how many ants will be there after :
i. 10 weeks
ii. 20 weeks

b)how many weeks will it take for the ant population to reach 2000.

a) (i) 1553 ants

(ii) 4823 ants

b) 12 weeks

Step-by-step explanation:

Given,

The initial number of ants, P = 500,

Also, the rate of increasing per week, r = 12% = 0.12,

So, the number of ants after x weeks,

a) (i) If x = 10 weeks,

The number of ants would be,

(ii) If x = 20 weeks,

The number of ants would be,

b) If A = 2000

Taking log both sides,

log(4) = xlog(1.12)

⇒ x =  12.23 ≈ 12 weeks

Step-by-step explanation:

For this exercise let "d" represents the number of days that it took the grass  in Jamie’s yard to grow one centimeter.

According to the information given in the exercise, you know that in ten days the grass grew sixteen centimeters.

Therefore, since it was growing at a constant rate, you can set up the following proportion:

Finally, you need to solve for "d" in order to find its value.

You get that this is:

Therefore, you can conclude that the grass  in Jamie’s yard grew 1 centimeter in 0.625 days.