a population grows according to the given logistic equation, where t is measured in weeks. (a) what is the carrying capacity? what is the value of k? (b) write the solution of the equation. (c) what is the population after 10 weeks?
Answer:Step-by-step explanation:P(t) = K / (1 + (K/P0 – 1) * e^(-rt))In this equation, P(t) is the population at time t, P0 is the initial population at time t=0, K is the carrying capacity, r is the intrinsic growth rate, and e is the base of the natural logarithm ( approximately 2.71828).To find the carrying capacity, you can set P(t) equal to K and solve for t. This will give you the time at which the population reaches its carrying capacity.To find the value of k, you can plug in the values for P(t), P0, and r and solve for K.To write the solution of the equation, you can solve for t by rearranging the equation and taking the natural logarithm of both sides.To find the population after 10 weeks, you can plug in the values for P0, K, r, and t=10 into the equation and solve for P(t).I hope this helps! Let me know if you have any further questions.