Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The population of a city increases by
1% per year. If this year's population is
p, which expression represents next year's population?

0.01 p

1p

1.01 p

1.001 p

The population of a city increases by $1 \%$ per year. If this year's population is $p$ , which expression represents next year's population? $\newline$ $0.01 p$ $\newline$ $1 p$ $\newline$ $1.01 p$ $\newline$ $1.001 p$

View step-by-step help

View step-by-step help

Exponential growth and decay: word problems

Full solution

Q. The population of a city increases by

1 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.01 p

\newline

1 p

\newline

1.01 p

\newline

1.001 p

Understand Population Increase: Understand the percentage increase in population. The population increases by $1\%$ per year. To find the population for the next year, we need to add this $1\%$ increase to the current population.
Convert to Decimal: Convert the percentage increase to a decimal. $\newline$ $1\%$ as a decimal is $0.01$ . This means that the increase in population is $0.01$ times the current population $p$ .
Calculate Next Year's Population: Calculate the population for the next year. $\newline$ To find the next year's population, we add the increase to the current population. This is equivalent to multiplying the current population by $1$ (which represents $100\%$ of the current population) plus the decimal equivalent of the increase (which is $0.01$ ). $\newline$ Next year's population = $p + (0.01 \times p) = p \times (1 + 0.01) = p \times 1.01$
Identify Correct Expression: Identify the correct expression. $\newline$ The correct expression that represents next year's population is $1.01 p$ .

More problems from Exponential growth and decay: word problems

Question

Solve. Write your answer as an integer or a fraction in simplest form.

\newline

5^x=1

\newline

x=

Posted 2 months ago

Question

Steven opened a savings account and deposited

\$100.00

as principal. The account earns

9\%

interest, compounded annually. What is the balance after

5

\newline

Use the formula

A = P(1 + \frac{r}{n})^{nt}

A

is the balance (final amount),

P

is the principal (starting amount),

r

is the interest rate expressed as a decimal,

n

is the number of times per year that the interest is compounded, and

t

is the time in years.

\newline

Round your answer to the nearest cent.

\newline

\$

Posted 2 months ago

Question

Use the following function rule to find

f(1)

\newline

f(x) = 12(7)^x + 8

\newline

f(1) =

Posted 1 month ago

Question

The town of Valley View conducted a census this year, which showed that it has a population of

1,800

people. Based on the census data, it is estimated that the population of Valley View will grow by

12\%

\newline

Write an exponential equation in the form

y = a(b)^x

that can model the town population,

y

x

decades after this census was taken.

\newline

Use whole numbers, decimals, or simplified fractions for the values of

a

b

\newline

y =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = 9^x

\newline

x =

Posted 2 months ago

Question

Solve. Round your answer to the nearest thousandth.

\newline

7 = e^x

\newline

x =

Posted 1 month ago

Question

Solve. Simplify your answer.

\newline

\log u = 1

\newline

u =

Posted 2 months ago

Question

Solve. Simplify your answer.

\newline

7\log x = 7

\newline

x =

Posted 1 month ago

Question

g(t) = 3^t

change over the interval from

t = 3

t = 4

\newline

\newline

g(t)

3

\newline

g(t)

3

\newline

g(t)

3\%

\newline

g(t)

200\%

Posted 2 months ago

Question

f(x)

6

over every unit interval in

x

f(0) = 0

\newline

Which could be a function rule for

f(x)

\newline

\newline

f(x) = 6^x

\newline

f(x) = 6x

\newline

f(x) = \frac{1}{6^x}

\newline

f(x) = \frac{x}{6}

Posted 2 months ago