Instructor-created question where t is in days. The relative (daily) growth rate

Question

Instructor-created question where t is in days. The relative (daily) growth rate is 4.2%. The current population is 326. A population of bacteria follows the continuous exponential growth model P(t) Po A) Find the growth model. (the function that represents the population after t days) P(t) B) Find the population exactly 1 weeks from now. Round to the nearest barium The population in 1 weeks will be C) Find the rate of change in the population exactly 1 weeks from now Round to the nearest unit The population will be increasing by aboutbacteria per day exactly 1 weeks from now. D) When will the popualtion reach 4978? ROUND TO 2 DECIMAL PLACES The population will reach 4978 aboutdays from now. Enter your answer in the edit fields and then click Check Answer. All parts showing Clear All Check Answer

Explanation / Answer

a) The population increases at the rate of 4.2% = 0.042

Hence the population after t days will be

P(t) = Po * (1+0.042)^t = 326 * (1.042)^t = 326* e^(t * ln(1.042)) = 326* e^(0.04114t)

b)

P(7) = Po * (1.042)^7 = 326 * (1.042)^7 = 434.802

Hence the nearest bacterium count will be 435

c)

P(t) = 326* e^(0.04114t)

P'(t) =326* 0.04114 * e^(0.04114t) = 13.411+4e^(0.04114t) = 13.411e^(0.04114 * 7) = 17.88

Hence the answer will be 18

d)

4978 = 326(1.042)^t

15.2699 = (1.042)^t

t = ln(15.2699)/ln(1.042) = 66.255

Hence the number of days will be 66.26

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

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