The fox population in a certain region has a continuous growth rate of 4 percent per year. It is estimathat the population in the year 2000 was 7200.(a) Find a function that models the population t years after 2000 (t =0 for 2000).Hint: Use an exponential function with base e.Your answer is P(t) = 7200X(b) Use the function from part (a) to estimate the fox population in the year 2008.Your answer is (the answer must be an integer) 9854X

The exponential growth model Initial population of fox.The population of fox at time t.Growth…

Answered: The fox population in a certain region…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.7: Applications

Problem 14EQ

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Similar questions

An investment account was opened with aninitial deposit of 9,600 and earns 7.4 interest,compounded continuously. How much will theaccount be worth after 15 years?
Suppose that $12,000 is invested in a saving account paying 5.6% interest per year. (a)Write the formula for the amount in the account after t years if interest is compounded monthly. (b)Find the amount in the after 3 years if interest is compounded daily. (c)How long will it take for the amount in the account to grow to $20,000 if interest iscompounded continuously?
A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, thesample has decayed to 80 grams. Rounding to fivesignificant digits, write an exponential equationrepresenting this situation. To the nearest day, whatis the half-life of this substance?
Table 2 shows a recent graduate’s credit card balance each month after graduation. a. Use exponential regression to fit a model to these data. b. If spending continues at this rate, what will the graduate’s credit card debt be one year after graduating?
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What is the y -intercept of the logistic growth model y=c1+aerx ? Show the steps for calculation. What does this point tell us about the population?
With what kind of exponential model would doubling time be associated? What role does doubling time play in these models?
Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine whetherthe data from the table would likely represent a function that is linear, exponential, or logarithmic.
Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to 2012. a. Let x represent time in years starting with x=0 for the year 1997. Let y represent the number of seals in thousands. Use logistic regression to fit a model to these data. b. Use the model to predict the seal population for the year 2020. c. To the nearest whole number, what is the limiting value of this model?
Use a graphing calculator to solve each problem. In Example 4, suppose that a birth control program changed the formula for poulation growth to Pt=1000e0.01t. How long will the food supply be adequate? EXAMPLE 4 Using a Graphing Calculator to Solve a popuiation Problem Suppose that a country with a population of 1000 people is growing exponentially according to the population function Pt=1000e0.02t Where t in years. Furthermore, assume that the food supply, measured in adequate food per day per person, is growing linearly according to the function fx=30.625x+2000 In how many years will the population outstrip the food supply?

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