please solve in Matlab

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P(t +1) = rP() (1 Peo) (1) The logistic map is a model that is often used in ecology to model population growth. It is defined by P(t) K Here, P(t) represents the population density of a given species at year t, the parameter r is a growth rate and the parameter K is the maximum possible population density (known as the carrying capac- ity). This equation says that if we know the density at one year, we can substitute it into the right hand side to find the population at the next year. For instance, if we knew the population at year 0 (given by P(0)), we could calculate 1 K P(1) = rP(O) (1-POOD P(2) ==P(1)(1-2) = 1- = = = Once we had the population density at year 1, we could then find the density at year 2 using P(1) K (a) Suppose that P(0) = 5, K = 10 and r = 2. Calculate P(3) and save it in a variable named A11. (b) Now suppose that P(0) = 10, K = 15 and r = 3. Calculate P(4) and save it in a variable named A12. (2) A slightly different version of this model, known as the Ricker model, is often used in fisheries biology. The Ricker model uses the formula P(t+1) = P(t)e"(1-P). (The function exp or np.exp might be useful in the following calculations.) (a) Suppose that P(0) = 5, K = 12 and r = 2. Calculate P(3) and save it in a variable named A13. (b) Now suppose that P(0) = 2, K = 25 and r = 2.5. Calculate P(4) and save it in a variable named A14. (c) Now suppose that P(0) = 0, K = 20 and r = 3.1. "Calculate P(500). (There won't be any calculations necessary for this one.) Save your answer in a variable named A15