let P(t) be the population of a colony of bacteria, where t is measured in days. Suppose that the initial population of the colony is 100 and it triples every four days. Assume growth is exponential.
(a)Find and simplify P(t)
(b)What is the size of the population after 10 days?
(c)When will the population reach 1000?
Please show all steps

Question

let P(t) be the population of a colony of bacteria, where t is measured in days. Suppose that the initial population of the colony is 100 and it triples every four days. Assume growth is exponential. 
(a)Find and simplify P(t)
(b)What is the size of the population after 10 days?
(c)When will the population reach 1000?
Please show all steps

wolf1728 · Answer

Pt = 100*3^(Days/4)

After 10 Days
Pt = 100*3^10/4
Pt = 100*3^2.5
Pt = 1,559

Population reaches 1,000?
Pt = 100*3^(Days/4)
(1,000 / 100) = 3^(Days/4)
log (1,000 / 100) = (Days/4) * log(3)
log (1,000 / 100) / log(3) = (Days / 4)
1 / 0.4771212547 =Days / 4
2.0959032743 = Days / 4
Days = 8.3836130972