(a) 6. The population (P) of Calcutonians (2000 of which currently reside in this blissful state of Calcutown) reproduce at a rate that is proportional to the Population at time t. If the reproduction rate is 17%, (your constant k), write the DE and use the method of separation of variables to show all steps to solve for the population function P(t). (b) Show all steps to determine the number of years that it takes for the population of Calcutown to double to 4000 blissful residents. Write a sentence to summarize your results.

A scientist is studying three different cultures of bacteria {labeled "A", "B" and "C"} and wants to mathematically model the bacterial change of each type. To do this, the scientist decides to collect data for 25 consecutive days and builds the following scatter diagrams where the horizontal axis corresponds to "t" and the vertical axis to the amount of bacteria present in the culture P = P (t) Help the scientist decide which mathematical model (initial value problem) to use for each of the three types of crops. To do this, associate each of the graphs above with one of the following initial value problems. Crop type A a) dP/dt = k with P(0)=P0 and k>0.b) dP/dt = k with P(0)=P0 and k<0.c) dP/dt = kt with P(0)=P0 and k>0.d) dP/dt = kt with P(0)=P0 and k<0.e) dP/dt = kP with P(0)=P0 and k>0.f) dP/dt = kP with P(0)=P0 and k<0.g) dP/dt = kP(1-P/M) with P(0)=P0 and M, k>0.h) dP/dt = kP(1-P/M) with P(0)=P0 and M, k<0. Crop type B a) dP/dt = k with P(0)=P0 and…

The total expenditures (in millions) of current dollars for pollution abatement and control during the period from 2000 through 2019 can be approximated by the function P(x) = 166.61 e 0.03x, where x = 0 corresponds to the year 2000. (a) In what year would the total expenditures reach $208 million dollars? (b) If this model remains accurate, when would the total expenditures reach $482 million? (a) The expenditures would reach $208 million in the year mid- (Simplify your answer. Type a whole number.)

A cell of some bacteria divides into two cells every 50 minutes. The initial population is 4 bacteria. (a) Find the size of the population after t hours y(t) = (function of t) (b) Find the size of the population after 8 hours. y(8): (c) When will the population reach 32? T =