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umka21 [38]
3 years ago
6

There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 anteaters, an

d the population of anteaters doubled every 3.6 weeks. How long into the voyage were there 200 ants per anteater? (Round your answer to one decimal place.)
Social Studies
1 answer:
patriot [66]3 years ago
6 0

Answer:

there will be 200 ants per anteater after 5.78 weeks.

Explanation:

As the question is not complete, the first part is missing from which the population of ants  at any given time is calculated as  y=400e^{0.56t}.

At the start t=0, y=17

now the equation of population is given as

y=a_1e^{b_1t}

Here a1=17 for calculation of b1 using the doubling time of 3.6 weeks.

y=a_1e^{b_1t}\\34=17e^{b_1*3.6}\\2=e^{b_1*3.6}\\b_1=ln(2)/3.6\\b_1=0.1925 week^{-1}

So the equation is given as y=17e^{0.19t}

Now by using the equation

\frac{200}{1}=\frac{400e^{0.56t}}{17e^{0.19t}}\\200*17=400e^{0.56t-0.19t}\\t=\frac{\ln \left(\frac{17}{2}\right)\cdot \:100}{37}\\t=5.78

So there will be 200 ants per anteater after 5.78 weeks.

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