A bacteria culture initially contains 100 cells and grows at a rate proportional

Question

A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 560.

(a) Find an expression for the number of bacteria after t hours.
p(t)=

(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest whole number.)
p(2)=

(c) Find the rate of growth after 2 hours. (Round your answer to the nearest whole number.)
p'(2)=

(d) When will the population reach 10,000? (Round your answer to one decimal place.)
t=

Explanation / Answer

The growth will be exponential, P(t)=Aexp(bt) at t=0 A=P(0)=100 p(1)=100exp(b)==>b=ln(5.6)=1.72 b) p(2)=100exp(1.72*2)=3118.7=3119 c)p'(t)=100*1.72*exp(1.72t) p'(2)=100*1.72*exp(1.72*2)=5364 d)p(t)=10000 10000=100exp(1.72t)==>exp(1.72t)=100==>1.72t= 4.6052==>t= 2.7

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.