912 points | Pravious Anawors UWAProCalot 12 P.009. My Notos A ship embarked on

Question

912 points | Pravious Anawors UWAProCalot 12 P.009. My Notos A ship embarked on a long voyage. At the start of the voyage, there were 500 ants in the cargo hold of the ship, One week into the voyage, there were 900 ants. Suppose the population of ants is an exponential function of time. (Round your answers to two decimal places.) (a) How long did it take the population to double? 1.1792 weeks (b) How long did it take the population to triple? 1.8691 weeks (c) When were there 10,000 ants on board? 5.0966 weeks (d) There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 15 anteaters, and the population of anteaters doubled every 2.5 weeks. How long into the voyage were there 200 ants per anteater? (Round your answer to one decimal place.) 9.2822 x weeks Additional Materials Reading

Explanation / Answer

d) writing population of anteaters as exponetial function

15*2 = 15 e^r(2.5)

r = 0.277259

equation of anteaters is

P = 15 e^0.277259 t

setting up the equation

15 e^0.277259 t  = 200 [ 500e^.083969t ]

solving for t

t = 45.6

so, there will be 200 ants per anteater after 45.6 weeks

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