Answer:
The answers to the question are
- How long did it take the population to double? Answer = one week
- How long did it take the population to triple? Answer = 1.58 weeks
- When were there 10, 000 ants on board? Answer = 5.06 weeks
- How long into the voyage were there 200 ants per anteater? Answer = 11.38 weeks
Step-by-step explanation:
To solve the question we use a similar analogy of half life calculation
Therefore we have
where
Number of ants after time t
Starting number of ants
Therefore
600 = 300 × 
= 2
㏑
= ㏑2
㏑<u>2 = ㏑2</u>
= 1 and t = 1 week
It took one week for the population of the ants to double
For the population to triple, we have
3×300 = 300× 
900 = 300× 
=3
x㏑2 =㏑3 or x =
= 1.58 weeks
There were 10000 ants onboard after
10000 = 300× 
or
=
and x = (㏑
)/㏑2 = 5.06 weeks
For the anteaters we have
Time for the anteaters to double = 3.2 weeks
Therefore t in the equation
= 3.2 weeks
and the length of time it took for the population of ant eaters to grow to 200 is given by
200 = 17×
=17×
From which we have
㏑2 = ㏑(200/17)
x = 3.2×3.56 = 11.38 weeks