Correct Answers are in bold please help me finish the problem and include your s
ID: 2911114 • Letter: C
Question
Correct Answers are in bold please help me finish the problem and include your steps please
1. A ship embarked on a long voyage. At the start of the voyage, there were 300 ants in the cargo hold of the ship. One week into the voyage, there were 600 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?
1.00 weeks
(b) How long did it take the population to triple?
1.58 weeks
(c) When were there 10,000 ants on board?
5.06 weeks
(d) There also was an exponentially-growing population of anteaters on board. At the start of the voyage there were 18 anteaters, and the population of anteaters doubled every 3.8 weeks. How long into the voyage were there 200 ants per anteater? (Round your answer to one decimal place.)
_____ weeks
2.The cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 21,000 people. In 1990, its population was 24,000. Bonipto had a population of 36,000 in 1980. The population of Bonipto doubles every 55 years. (Round your answers to the nearest whole number.)
(a) How long does it take the population of Abnarca to double?
52 yr
(b) How long will it take for Abnarca's population to equal that of Bonipto?
Explanation / Answer
y= a bx
points are (0,300) and (1,600)
300=a b0
a=300
600=300b1
b=2
y=300(2)x
a. Double means y=600
600=300(2)x
2x=2
x=2
b.Triple means y=600
600=200(2)x
3=2x
x=log(3)/log(2)
x=1.58week
c. 10000=300(2)x
100/3=2x
log(100/3)/log 2=x
x=5.06weeks
d. 36=18(b)3.8
b=21/3.8
y=18(2)x/3.8
200=18(2)x/3.8
x=13.2