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For the following exercises, use the logistic growth model
Determine whether the data from the table could best be represented as a
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College Algebra By Openstax
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- For the following exercises, use the logistic growth model f(x)=1501+8e2x . Graph the model.arrow_forwardFor the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. Suppose an investment account is opened with an initial deposit of 12,000 earning 7.2 interest compounded continuously. How much will the account be worth after 30 years?arrow_forwardFor the following exercises, refer to Table 10. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form y=a+bln(x) that best fits the data in the table.arrow_forward
- For the following exercises, use the logistic growth model f(x)=1501+8e2x . Rewrite f(x)=1.68(0.65)x as an exponential equation with base e to five significant digits.arrow_forwardFor the following exercises, use the logistic growth model f(x)=1501+8e2x . Find and interpret f(4). Round to the nearest tenth.arrow_forwardThe 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.arrow_forward
- For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic.arrow_forwardFor the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic.arrow_forwardHector invests $10,000 at age 21. He hopes the investments will be worth when he turns 50. If the interest compounds continuously, approximately what rate of growth Will he need to achieve his goal?arrow_forward
- For the following exercises, determine whether the equation represents continuous growth, continuous decay, or neither. Explain. How much less would the account from Exercise 42 be worth after 30 years if it were compounded monthly instead?arrow_forwardFor the following exercises, refer to Table 11. Use the LOGISTIC regression option to find a logistic growth model of the form y=c1+aebx that best fits the data in the table.arrow_forwardFor the following exercises, refer to Table 9. Use the LOGarithm option of the REGression feature to find a logarithmic function of the form y=a+bln(x) that best fits the data in the table.arrow_forward