Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Does the function model exponential growth or decay?

f(t)=(1)/(4)*4^(t)
Choose 1 answer:
(A) Growth
(B) Decay

Does the function model exponential growth or decay? $\newline$ $f(t)=\frac{1}{4} \cdot 4^{t}$ $\newline$ Choose $1$ answer: $\newline$ (A) Growth $\newline$ (B) Decay

View step-by-step help

View step-by-step help

Interpret the exponential function word problem

Full solution

Q. Does the function model exponential growth or decay?

\newline

f(t)=\frac{1}{4} \cdot 4^{t}

\newline

Choose

1

answer:

\newline

(A) Growth

\newline

(B) Decay

Base of Exponent: Step $1$ : To determine if the function represents growth or decay, we need to look at the base of the exponent. In the function $f(t)=\frac{1}{4}\cdot4^{t}$ , the base of the exponent is $4$ .
Exponential Growth or Decay: Step $2$ : If the base of the exponent is greater than $1$ , the function models exponential growth. If the base is between $0$ and $1$ , the function models exponential decay.
Exponential Growth Determination: Step $3$ : Since the base of the exponent in our function is $4$ , which is greater than $1$ , the function models exponential growth.
Coefficient Impact: Step $4$ : The coefficient $\frac{1}{4}$ in front of the exponential function does not affect whether the function is growth or decay; it only affects the scale of the function.

More problems from Interpret the exponential function word problem

Question

13 \mathrm{~km}

stretch of road needs repairs. Workers can repair

3 \frac{1}{2} \mathrm{~km}

of road per week.

\newline

How many weeks will it take to repair this stretch of road?

\newline

Posted 4 months ago

Question

Liam opened a savings account and deposited

\$ 6000

. The account earns

5 \%

in interest annually. He makes no further deposits and does not withdraw any money. In

t

\$ 8865

in this account.

\newline

Write an equation in terms of

t

that models the situation.

Posted 4 months ago

Question

Samantha opened a savings account and deposited

\$ 8192

. The account earns

10 \%

in interest annually. She makes no further deposits and does not withdraw any money. In

t

\$ 25,710

in this account.

\newline

Write an equation in terms of

t

that models the situation.

Posted 4 months ago

Question

The graph of a sinusoidal function intersects its midline at

(0,-7)

and then has a minimum point at

\left(\frac{\pi}{4},-9\right)

\newline

Write the formula of the function, where

x

is entered in radians.

\newline

f(x)=

Posted 4 months ago

Question

The following formula is used in economics to find a company's gross profit rate

P

S

is the net sales and

C

is the cost of goods sold.

\newline

P=\frac{S-C}{S}

\newline

Rearrange the formula to highlight the cost of goods sold.

\newline

C=\square

Posted 4 months ago

Question

3 \cdot 5^{0.2 w}=720

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

w \approx

Posted 4 months ago

Question

18 \cdot 2^{5 t}=261

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

t \approx

Posted 4 months ago

Question

-4 \cdot 3^{6 w}=-1750

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

w \approx

Posted 4 months ago

Question

20 \cdot 7^{3 y}=5

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

y \approx

Posted 4 months ago

Question

10 \cdot 3^{\frac{5 t}{4}}=800

\newline

What is the solution of the equation?

\newline

Round your answer, if necessary, to the nearest thousandth.

\newline

t \approx

Posted 4 months ago