Show all necessary solutions. 1. A scientist working in Africa discovered that in a particular safari, the carrying capacity is 2,000 tigers. Five hundred tigers where then released into the safari. The growth of the tiger pack is modeled by the logistic equation 2000 P(t) : 1+ 3e-0.145t where t is the time in months. (a) Estimate the tiger population after 6 months. (b) After how many months will the tiger population reach 1,500. 2. A new species of animal was discovered to initially have a population of 215. After 10 years of uninhibited growth, the population rose to 1,134. Write an exponential function that approximately models the population of this species.

Show all necessary solutions. 1. A scientist working in Africa discovered that in a particular safari, the carrying capacity is 2,000 tigers. Five hundred tigers where then released into the safari. The growth of the tiger pack is modeled by the logistic equation 2000 P(t) : 1+ 3e-0.145t where t is the time in months. (a) Estimate the tiger population after 6 months. (b) After how many months will the tiger population reach 1,500. 2. A new species of animal was discovered to initially have a population of 215. After 10 years of uninhibited growth, the population rose to 1,134. Write an exponential function that approximately models the population of this species.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 15DE

See similar textbooks

Similar questions

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?
Buffalo: Waterton Lakes National Park of Canada, where the Great Plains dramatically meet the Rocky Mountains in Alberta, has a migratory buffalo bison herd that spends falls and winters in the park. The herd is currently managed and so kept small; however, if it were unmanaged and allowed to grow, then the number N of buffalo in the herd could be estimated by the logistic formula N=3151+14e0.23t Here t is the number of years since the beginning of 2002, the first year the herd is unmanaged. a. Make a graph of N versus t covering the next 30 years of the herds existance corresponding to dates up to 2032. b. How many buffalo are in the herd at the beginning of 2002? c. When will the number of buffalo first exceed 300?. d. How many buffalo will there eventually be in the herd? e. When is the graph of N, as a function of t, concave up? When is it concave down? What does this mean in terms of the growth of the buffalo herd?.
The population of a lake of fish is modeled by the logistic equation P(t)=16,1201+25e0.75t, where t is time inyears. To the unrest hundredth, how manyyears will it take the lake to reach 80% of its carrying capacity?For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table.Observe the shape of the scatter diagram to determine whether the data is best described by an exponential,logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models thedata. When necessary, round values to five decimal places.
What is the carrying capacity for a population modeled by the logistic equation P(t)=250,0001+499e0.45t ? initial population for the model?
Rachel invests $15,000 at age 25. She hopes the investments will be worth when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal?
The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is in
Jerome invests $18,000 at age 17. He hopes the investments will be worth $30,000 when he turns 26. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Is that a reasonable expectation?
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?