Question

Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose that P(t) satisfies the differential equation P' = .01P(t), P(0) = 3. (a) Find the formula for P(t). P(t) = (Type an exact answer.) (b) What was the initial population, that is, the population in 1990? The initial population was million. (c) What is the growth constant? The growth constant is . (d) What was the population in 1997? The population in 1997 was million. (Round to two decimal places as needed.) (e) Use the differential equation to determine how fast the population is growing when it reaches 4 million people. The growth rate is people per year. (f) How large is the population when it is growing at the rate of 80,000 people per year? The population is million.

          Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose that P(t) satisfies the differential equation P' = .01P(t), P(0) = 3.

(a) Find the formula for P(t).
P(t) = (Type an exact answer.)

(b) What was the initial population, that is, the population in 1990?
The initial population was million.

(c) What is the growth constant?
The growth constant is .

(d) What was the population in 1997?
The population in 1997 was million. (Round to two decimal places as needed.)

(e) Use the differential equation to determine how fast the population is growing when it reaches 4 million people.
The growth rate is people per year.

(f) How large is the population when it is growing at the rate of 80,000 people per year?
The population is million.

Let P(t) be the population (in millions) of a certain city t years after 1990, and suppose that P(t) satisfies the differential equation P' = .01P(t), P(0) = 3.

(a) Find the formula for P(t).
P(t) = (Type an exact answer.)

(b) What was the initial population, that is, the population in 1990?
The initial population was million.

(c) What is the growth constant?
The growth constant is .

(d) What was the population in 1997?
The population in 1997 was million. (Round to two decimal places as needed.)

(e) Use the differential equation to determine how fast the population is growing when it reaches 4 million people.
The growth rate is people per year.

(f) How large is the population when it is growing at the rate of 80,000 people per year?
The population is million.

Added by Francisca S.

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