Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differentialequation P'(t) = 0.04P(t), P(0) = 7.(a) Use the differential equation to determine how fast the population is growing when it reaches 10 million people.(b) Use the differential equation to determine the population size when it is growing at a rate of 600,000 people peryear.(c) Find a formula for P(t).(a) Choose the correct process to find how fast the population is growing when it reaches 10 million people.A. Evaluate P'(t) = 0.04(10).B. Evaluate P'(t) = 0.04P(10).C. Solve 10 =0.04P(t) for P(t).D. Solve P'(10) = 0.04P(t) for P(t).

(a) Choose the correct process to find how fast the population is growing when it reaches 10 million people. O A. Evaluate P'(t) = 0.04(10). B. Evaluate P'(t) = 0.04P(10). C. Solve 10 =0.04P(t) for P(t). D. Solve P'(10) = 0.04P(t) for P(t).

(a) Choose the correct process to find how fast the population is growing when it reaches 10 million people. O A. Evaluate P'(t) = 0.04(10). B. Evaluate P'(t) = 0.04P(10). C. Solve 10 =0.04P(t) for P(t). D. Solve P'(10) = 0.04P(t) for P(t).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Let P(t) be the population (in millions) of a certain city t years after 2015, and suppose that P(t) satisfies the differential
equation P'(t) = 0.04P(t), P(0) = 7.
(a) Use the differential equation to determine how fast the population is growing when it reaches 10 million people.
(b) Use the differential equation to determine the population size when it is growing at a rate of 600,000 people per
year.
(c) Find a formula for P(t).
(a) Choose the correct process to find how fast the population is growing when it reaches 10 million people.
A. Evaluate P'(t) = 0.04(10).
B. Evaluate P'(t) = 0.04P(10).
C. Solve 10 =0.04P(t) for P(t).
D. Solve P'(10) = 0.04P(t) for P(t).

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