/3 points SPreCalc7 4.6.013. Ask Your Teacher My Notes Question Part Points Subm

Question

/3 pointsSPreCalc7 4.6.013.

Ask Your Teacher

My Notes

Question Part Points Submissions Used This exercise uses the population growth model. A culture starts with 8000 bacteria. After 1 hour the count is 10,000 (a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.) n(t) = (b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) bacteria (c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) Need Help? ReadIt Watch It Submit Answer Save Progress Practice Another Version 5. +-4 points SPreCalc7 4.6.017 My Notes Ask Your Teac This exercise uses the radioactive decay model. The half-life of radium-226 is 1600 years. Suppose we have a 29-mg sample (a) Find a function m(t)- mo2h that models the mass remaining after t years m(t) = (b) Find a function m(t)mthat models the mass remaining after t years. (Round your r value to six decimal places.) m(t) = (c) How much of the sample vwill remain after 4000 years? (Round your answer to one decimal place.) ng (d) After how many years will only 19 mg of the sample remain? (Round your answer to one decimal place.) yr Need Help? Read It Watch

Explanation / Answer

Let N(t) denotes bacteria count after time t hours N(t) = N0 e^ (kt) N0 Initial Bacteria count ( 8000) k growth rate t time elapsed in hours From data in question 10000 = 8000* (e^k) 1.25 = e^k Taking natural log both sides we get 0.2231436 = k Now number of bactera after 2 hours is N (2) = 8000* e^ 2* k = 12500 Bacteria Number of hours needed for bacteria to duble is 2N0 = N0*e*kt 2 = e^kt Taking natural log both sides 0.6931472 = 0.223t t = 3.106284 years Solution

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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