A population P obeys the logistic model. It satisfies the equation dP 2 · P(13 – P) for P > 0. dt 1300 (a) The population is increasing when (c) Assume that P(0) 4. Find P(46). = P(46) =
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- What is the y -intercept on the graph of the logistic model given in the previous exercise?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?Recall 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 .
- The 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.bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.Does the equation y=2.294e0.654t representcontinuous growth, continuous decay, or neither?Explain.
- Assume a simple logistic regression model for X and Y. We know: bo= -1.1 and b₁ = 0.4 Estimate P(Y= 1) when X = 1.A red maple sapling was 3 feet tall when planted in 2010. Six years later, the tree was 18 feet tall. The growth rate of the tree is constant over time. Find a linear model for the height H (in ft) of the red maple t years after 2010. Let t = 0 represent 2010. H = What is the expected height (in ft) of the red maple in 2020? ftLet f(1) = 2 and "(1) = 3. Suppose g(a) = f(a)]. Calculate g(1). %3D
- Log(Wagei) = α + β1Educationi + β2Femalei + β3Non Whitei + β4Educationi × Femalei + εi For males, and holding other variables constant, the regression output from the linear regression model above implies that an extra year of education is associated with what percent change in wages?Consider the following estimated model, where the dependent variable is the log of the hourly wage: log(wage) = 0.417 - 0.238female + 0.17educ + 0.0232 exper - 0.00058exper? +0.0295tenure – 0.00059tenure? female 1 if the person is female, and 0 if the person is male educ = level of education, in years exper = level of expertise, in years tenure = duration of tenure, in years Given that the above regression model has 313 observations, then its degrees of freedom is equal to For the same levels of education, expertise, and tenure, women earn exactly % less compared to men, holding other factors fixed.Use the following information to answer questions 4 & 5: The following table is adapted from a paramecium culture experiment. The data show the paramecium population N as a function of time t in days. 3 5 6 8 9 10 11 t 2 N 11 33 91 188 328 | 415 | 507 577