Suppose that a certain population grows according to an exponential model.(a) Write the differential equation for this situation with a relative growth rate of k = 0.01. Produce a solution for the initial condition t = 0 (in hours) and population P = 1 (in thousands).(b) Find the population when t = 10 hours, t = 100 hours, and t = 1000 hours.(c) After how many hours does the population reach 2 thousand? 30 thousand? 55 thousand?
(d) As the time t increases without bound, what happens to the population?
(e) Sketch the graph of the solution of the differential equation.

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The Answer of Suppose that a certain population grows according to an exponential model.(a) Write the differential equation for this situation with a relative growth rate of k = 0.01. Produce a solution for the initial condition t = 0 (in hours) and population P = 1 (in thousands).(b) Find the population when t = 10 hours, t = 100 hours, and t = 1000 hours.(c) After how many hours does the population reach 2 thousand? 30 thousand? 55 thousand?
(d) As the time t increases without bound, what happens to the population?
(e) Sketch the graph of the solution of the differential equation.

Suppose That a Certain Population Grows According to an Exponential