Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

There are two cubes. The first cube has a volume of $1,000$ cubic units. The second cube is smaller than the first, with sides only half as long. What is the volume of the second cube? $\newline$ $\_\_\_\_\_\_\_$ cubic units

View step-by-step help

View step-by-step help

Exponential growth and decay: word problems

Full solution

Q. There are two cubes. The first cube has a volume of

1,000

cubic units. The second cube is smaller than the first, with sides only half as long. What is the volume of the second cube?

\newline

\_\_\_\_\_\_\_

cubic units

Calculate first cube side: Calculate the side length of the first cube. $\newline$ Since the volume of a cube is given by $side^3$ , we find the side length of the first cube by taking the cube root of $1,000$ . $\newline$ $side = \text{cube root of } 1,000 = 10$ units.
Determine second cube side: Determine the side length of the second cube. $\newline$ The second cube's sides are half as long as the first cube's sides. $\newline$ side of second cube = $\frac{10}{2} = 5$ units.
Calculate second cube volume: Calculate the volume of the second cube. $\newline$ Volume of the second cube = $\text{side}^3 = 5^3 = 125$ cubic units.

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 1 month 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