Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

How does $h(x) = 10^x$ change over the interval from $x = 5$ to $x = 6$ ? $\newline$ Choices: $\newline$ (A) $h(x)$ increases by $10\%$ $\newline$ (B) $h(x)$ increases by $900\%$ $\newline$ (C) $h(x)$ increases by $10$ $\newline$ (D) $h(x)$ decreases by $10$

View step-by-step help

View step-by-step help

Full solution

Q. How does

h(x) = 10^x

change over the interval from

x = 5

to

x = 6

?

\newline

Choices:

\newline

(A)

h(x)

increases by

10\%

\newline

(B)

h(x)

increases by

900\%

\newline

(C)

h(x)

increases by

10

\newline

(D)

h(x)

decreases by

10

Calculate $h(6)$ : Now, calculate $h(6)$ which is $10^6$ . $\newline$ $h(6) = 10^6 = 1,000,000.$
Find increase: Find the increase from $h(5)$ to $h(6)$ . $\newline$ Increase = $h(6) - h(5) = 1,000,000 - 100,000 = 900,000$ .
Determine percentage increase: Determine the percentage increase. $\newline$ Percentage increase = $(\text{Increase} / h(5)) \times 100\%$ = $(900,000 / 100,000) \times 100\%$ = $900\%$ .

More problems from Power rule

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 2 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 1 month ago

Question

\newline

32^{(-1/5)}

Posted 1 month ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 2 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 1 month ago