# How do you solve net population growth word problems?

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It is projected that t years from now the population of a certain country will be changing at the rate of e^(0.02 t) million per year. If the current population is 50 million, what will be the population 10 years from now?

It is projected that t years from now the population of a certain country will be changing at the rate of e^(0.02 t) million per year. If the current population is 50 million, what will be the population 10 years from now?

I will solve this question using year by year basis

The first year's end is P1=e^0.0250 million = 51,010.067; the second year's end is P2=e^0.0251,010,067 = 52,040,539; the tenth year's end is P10=e^0.02*P9 = 61,070,140.

P10 = (e^(0.0210))P0 = 61,070,138, to put it simply.

P = P0e^(rt) is the general exponential growth formula.

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To solve net population growth word problems, you typically follow these steps:

- Identify the initial population (P) and the growth rate (r), usually expressed as a percentage.
- Determine the time period (t) over which the population is growing.
- Use the formula for exponential growth: ( P(t) = P_0 \times (1 + r)^t ), where ( P(t) ) is the final population after time t, ( P_0 ) is the initial population, and r is the growth rate expressed as a decimal.
- Substitute the values into the formula and calculate the final population.

If the problem involves a population decreasing over time, you can use the formula for exponential decay: ( P(t) = P_0 \times (1 - r)^t ), where r is the decay rate expressed as a decimal.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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