A ship embarked on a long voyage. At the start of the voyage, there were 400 ant
ID: 3014260 • Letter: A
Question
A ship embarked on a long voyage. At the start of the voyage, there were 400 ants in the cargo hold of the ship. One week into the voyage, there were 700 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?
( in weeks)
(b) How long did it take the population to triple?
in weeks
(c) When were there 10,000 ants on board?
in weeks
(d) There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 17 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.)
in weeks
(PLEASE DO NOT COPY OTHERS ANSWERS AND POST THEM FOR ME!!!! PLEASE DO NOT POST WRONG ANSWERS)
Explanation / Answer
writing the given data in point form
(0,400),(7,700)
exponential functions are of the form
y= a bx
a=400
700=400 b7
b=1.083
The function is
y= 400(1.083)x
a. Double of 400 is 800
800=400(1.083)x
log 2=x log 1.083
x=8.69 days
b. triple of 400=1200
1200=400 1.083x
log 3=x log 1.083
x=13.78 days
c. 10000=400* 1.083x
log 25=x log 1.083
x=40.37 days
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