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Graph the following logistic function, first discussed in Example 5. Use
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College Algebra (MindTap Course List)
- The population of a culture of bacteria is modeled by the logistic equation P(t)=14,2501+29e0.62t where t is inarrow_forwardRecall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such that the initial population at time t=0 is P(0)=P0. Show algebraically that cP(t)P(t)=cP0P0ebt .arrow_forwardUse the result from the previous exercise to graph the logistic model P(t)=201+4e0.5t along with its inverse on the same axis. What are the intercepts and asymptotes of each function?arrow_forward
- To the nearest whole number, what is the initial value of a population modeled by the logistic equation P(t)=1751+6.995e0.68t ? What is the carrying capacity?arrow_forwardThe natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.arrow_forwardThe formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.arrow_forward
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