**Problem 6: Exponential Growth of a Bacteria Culture**Consider a bacteria culture growing exponentially, with time measured in hours. Suppose $ P(0) = 100 $ cells is the initial size, and $ k = 0.03 $ is the relative growth rate.**Tasks:**1. **Determine $ P(10) $, the population size at 10 hours.** 2. **Determine $ P'(10) $, the growth rate for the population at 10 hours.** 3. **At what time $ t $ will the population reach 20,000 cells?**Include the units of measurement in your answers.

Answered: Image /qna-images/answer/8d01967f-eea4-470d-b976-62d9728432f5.jpg

Answered: 6. Consider a bacteria culture growing…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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3. A wildlife manager counted 1800 mice in a 10-km² area of forest. It is predicted that the mouse population in this area will grow exponentially according to the function P(t) = 1800e 0.03/ where P(t) is the > years. mouse population and t is the time, in a) How long will it take for the mouse population to i) double ii) triple b) Find the rate of change of the mouse population after i) 10 years ii) 25 years c) At what rate is the mouse population growing at the time when its number has tripled?
The table shows the age-adjusted death rates per 100,000 citizens for heart disease in a certain country. Complete parts (a) and (b) below. (a) Find an exponential model of the form f(t)=yob' for these data, where t=0 corresponds to the year 2000.Use the first and last data points to find a function. 1(t)=¹ (Round to two decimal places as needed.) (b) Assuming the model remains accurate, estimate the death rate in 2019 and 2024. The death rate in 2019 will be (Round to one decimal place as needed.) people per 100,000 The death rate in 2024 will be (Round to one decimal place as needed.) people per 100,000. Year 2000 2002 2004 2006 2008 2010 2012 2014 Death Rate 257.4 239.4 215.0 211.9 185.6 178.9 171.8 166.0
Suppose that P, is invested in a savings account in which interest is compounded continuously at 5.7% per year. That is, the balance dp P grows at the rate given by P = .057P(t) dt a) Find the function P(t) that satisfies the equation. b) Suppose that $1500 is invested. What is the balance after 3 years? 12
You plan to invest in an account which pays 6.5% compounded continuously. If the investment period is for 8 years, then A(P) = Pe 0.065 •8 = Pe 0.52 gives the total balance of P dollars. a. Find a formula for A'(P). b. Find and interpret A'(8000). c. Compare the approximation to the actual change. a. A'(P) = e0.52 (Type an exact answer in terms of e.) b. A'(8000) = 1.68 dollars increased in the total amount per dollar increase in the initial investment (Round to the nearest cent as needed.) Interpret A'(8000) = 1.68 GA. The future value of a 9 year investment of $8000 will be $ more than the future value of a 9 year investment of S8000. O B. The future value of a 9 year investment of $8001 will be $ more than the future value of a 9 year investment of S8000. O C. The future value of 8 year investment of $8000 at 7.5% will be $ more than the future value of a 8 year investment of $4000 at 6.5%. D. The future value of a 8 year investment of $8001 will be $ 1.68 more than the future value…
The population of an aquatic species in a certain body of water is approximated by the logistic function 37,500 where t is measured in years. Find G(t) = = ,-0.56t' the population and its growth rate at the following times. a. 1 year b. 5 years c. 12 years d. What happens to the rate of growth over time? 1 + 12e The population in 1 year is 4774 . (Round to the nearest whole number.) The population in 5 years is 21680. (Round to the nearest whole number.) The population in 12 years is 36965. (Round to the nearest whole number.) The growth rate in 1 year is per year. (Round to the nearest whole number.)
A tree farm starts with ten trees. Tree growth is expected to follow logistic growth with a first-order growth rate constant of r = 0.16 yr ' to a maximum of 8,000 trees. Write the equation that relates the number of trees (N) to time (1). What are the values of No, r, and K? Plot the number of trees over time if no harvesting occurs. Go out to about 70 years. What is the maximum sustainable yield (MSY)? How long should you wait before harvesting at the MSY? Determine the standing crop. (The standing crop is the number of trees at steady state when harvesting at the MSY.)

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