Math / Algebra

QuestionThe population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1989. Your answer is $\square$ billion

Studdy Solution

STEP 1

What is this asking? If the world population grows by 2% each year, starting from 5 billion in 1987, what will the population be in 1989? Watch out! Don't forget that two years pass between 1987 and 1989!

STEP 2

1. Find the growth factor.
2. Calculate the population in 1988.
3. Calculate the population in 1989.

STEP 3

We're given that the annual growth rate is 2%.
This means each year, the population is multiplied by $1 + 0.02 = \mathbf{1.02}$ .
This is our growth factor!
It's what we multiply by to get the next year's population.

STEP 4

We start with a population of $5$ billion in 1987.

STEP 5

To find the population in 1988, we multiply the 1987 population by the growth factor we found earlier: $5 \cdot 1.02 = \mathbf{5.1}$ So, the population in 1988 is $\mathbf{5.1}$ billion.

STEP 6

Now, we'll do the same thing again to find the population in 1989.
We'll multiply the 1988 population by our growth factor of $1.02$ : $5.1 \cdot 1.02 = \mathbf{5.202}$ Therefore, the projected world population in 1989 is $\mathbf{5.202}$ billion!

STEP 7

The projected world population in 1989 is $\mathbf{5.202}$ billion.

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QuestionThe population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1989. Your answer is $\square$ billion

Studdy Solution

STEP 1

What is this asking? If the world population grows by 2% each year, starting from 5 billion in 1987, what will the population be in 1989? Watch out! Don't forget that two years pass between 1987 and 1989!

STEP 2

1. Find the growth factor.
2. Calculate the population in 1988.
3. Calculate the population in 1989.

STEP 3

We're given that the annual growth rate is 2%.
This means each year, the population is multiplied by $1 + 0.02 = \mathbf{1.02}$ .
This is our growth factor!
It's what we multiply by to get the next year's population.

STEP 4

We start with a population of $5$ billion in 1987.

STEP 5

To find the population in 1988, we multiply the 1987 population by the growth factor we found earlier: $5 \cdot 1.02 = \mathbf{5.1}$ So, the population in 1988 is $\mathbf{5.1}$ billion.

STEP 6

Now, we'll do the same thing again to find the population in 1989.
We'll multiply the 1988 population by our growth factor of $1.02$ : $5.1 \cdot 1.02 = \mathbf{5.202}$ Therefore, the projected world population in 1989 is $\mathbf{5.202}$ billion!

STEP 7

The projected world population in 1989 is $\mathbf{5.202}$ billion.

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QuestionThe population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1989. Your answer is □\square□ billion

Studdy Solution

STEP 1

What is this asking? If the world population grows by **2%** each year, starting from **5 billion** in 1987, what will the population be in 1989? Watch out! Don't forget that two years pass between 1987 and 1989!

STEP 2

1. Find the growth factor.2. Calculate the population in 1988.3. Calculate the population in 1989.

STEP 3

We're given that the annual growth rate is **2%**.This means each year, the population is multiplied by 1+0.02=1.021 + 0.02 = \mathbf{1.02}1+0.02=1.02.This is our **growth factor**!It's what we multiply by to get the next year's population.

STEP 4

We **start** with a population of 555 billion in 1987.

STEP 5

To find the population in 1988, we **multiply** the 1987 population by the **growth factor** we found earlier: 5⋅1.02=5.15 \cdot 1.02 = \mathbf{5.1}5⋅1.02=5.1 So, the population in 1988 is 5.1\mathbf{5.1}5.1 billion.

STEP 6

Now, we'll do the same thing again to find the population in 1989.We'll **multiply** the 1988 population by our **growth factor** of 1.021.021.02: 5.1⋅1.02=5.2025.1 \cdot 1.02 = \mathbf{5.202}5.1⋅1.02=5.202 Therefore, the projected world population in 1989 is 5.202\mathbf{5.202}5.202 billion!

STEP 7

The projected world population in 1989 is 5.202\mathbf{5.202}5.202 billion.

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QuestionThe population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1989. Your answer is $\square$ billion

What is this asking? If the world population grows by 2% each year, starting from 5 billion in 1987, what will the population be in 1989? Watch out! Don't forget that two years pass between 1987 and 1989!

1. Find the growth factor.
2. Calculate the population in 1988.
3. Calculate the population in 1989.

We're given that the annual growth rate is 2%.
This means each year, the population is multiplied by $1 + 0.02 = \mathbf{1.02}$ .
This is our growth factor!
It's what we multiply by to get the next year's population.

We start with a population of $5$ billion in 1987.

To find the population in 1988, we multiply the 1987 population by the growth factor we found earlier: $5 \cdot 1.02 = \mathbf{5.1}$ So, the population in 1988 is $\mathbf{5.1}$ billion.

Now, we'll do the same thing again to find the population in 1989.
We'll multiply the 1988 population by our growth factor of $1.02$ : $5.1 \cdot 1.02 = \mathbf{5.202}$ Therefore, the projected world population in 1989 is $\mathbf{5.202}$ billion!

The projected world population in 1989 is $\mathbf{5.202}$ billion.