Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Eva deposited $50$ $\$$ in an account earning $10\%$ interest compounded annually. To the nearest cent, how much interest will she earn in $2$ years? $\$$ ____

View step-by-step help

View step-by-step help

Exponential growth and decay: word problems

Full solution

Q. Eva deposited

50

\$

in an account earning

10\%

interest compounded annually. To the nearest cent, how much interest will she earn in

2

years?

\$

____

Substitute values into formula: We substitute the given values into the compound interest formula: $\newline$ $A = P(1 + r/n)^{nt}$ $\newline$ $A = 50(1 + 0.10/1)^{1*2}$ $\newline$ $A = 50(1 + 0.10)^2$ $\newline$ $A = 50(1.10)^2$ $\newline$ Now we calculate $(1.10)^2$ .
Calculate $(1.10)^2$ : $(1.10)^2 = 1.10 \times 1.10 = 1.21$ Now we multiply this by the principal amount, $\$50$ . $A = 50 \times 1.21$
Multiply by principal amount: $A = 50 \times 1.21 = \$60.50$ $\newline$ This is the total amount in the account after $2$ years, including the initial deposit and the interest earned. $\newline$ To find the interest earned, we subtract the initial deposit from the total amount. $\newline$ Interest earned = $A - P$ $\newline$ Interest earned = $\$60.50 - \$50$
Find interest earned: Interest earned = $\$60.50$ - $\$50$ = $\$10.50$ $\newline$ Eva will earn $\$10.50$ in interest after $2$ years.

More problems from Exponential growth and decay: word problems

Question

Each year, Francesca earns a salary that is

2 \%

higher than her previous year's salary. In her first

5

years at this job, she earned a total of

\$ 187,345

\newline

What was Francesca's salary in her

1^{\text {st }}

year at this job?

\newline

Round your final answer to the nearest thousand.

\newline

Posted 4 months ago

Question

Every chemical element goes through natural exponential decay, which means that over time its atoms fall apart. The speed of each element's decay is described by its half-life, which is the amount of time it takes for the number of radioactive atoms of this element to be reduced by half.

\newline

The half-life of the isotope beryllium-

11

14

seconds. A sample of beryllium-

11

was first measured to have

800

t

seconds, there were only

50

atoms of this isotope remaining.

\newline

Write an equation in terms of

t

that models the situation.

Posted 4 months ago

Question

The following formula gives the temperature's measure in degrees Fahrenheit

F

C

is the measure in degrees Celsius:

\newline

F=\frac{9}{5} C+32

\newline

Rearrange the formula to highlight the measure in degrees Celsius.

\newline

C=

Posted 4 months ago

Question

2010

, the town of Fall River has been experiencing a growth in population.

\newline

The relationship between the elapsed time,

t

, in years, since

2010

and the town's population,

P(t)

, is modeled by the following function.

\newline

P(t)=36,800 \cdot 2^{\frac{t}{25}}

\newline

According to the model, what will the population of Fall River be in

2020

\newline

Round your answer, if necessary, to the nearest whole number.

\newline

Posted 4 months ago

Question

A huge ice glacier in the Himalayas initially covered an area of

45

square kilometers. Because of changing weather patterns, this glacier begins to melt, and the area it covers begins to decrease exponentially.

\newline

The relationship between

A

, the area of the glacier in square kilometers, and

t

, the number of years the glacier has been melting, is modeled by the following equation.

\newline

A=45 e^{-0.05 t}

\newline

How many years will it take for the area of the glacier to decrease to

15

square kilometers?

\newline

Give an exact answer expressed as a natural logarithm.

\newline

Posted 4 months ago

Question

Enzo is studying the black bear population at a large national park.

\newline

He finds that the relationship between the elapsed time

t

, in years, since the beginning of the study, and the black bear population

B(t)

, in the park is modeled by the following function.

\newline

B(t)=2500 \cdot 2^{0.01 t}

\newline

According to the model, what will the black bear population be at that national park in

25

years? Round your answer, if necessary, to the nearest whole number.

\newline

Posted 4 months ago

Question

Find the following trigonometric values.

\newline

Express your answers exactly.

\newline

\begin{array}{l} \cos \left(150^{\circ}\right)= \\ \sin \left(150^{\circ}\right)= \end{array}

Posted 4 months ago

Question

The moon's illumination changes in a periodic way that can be modeled by a trigonometric function.

\newline

On the night of a full moon, the moon provides about

0

25

lux of illumination (lux is the SI unit of illuminance). During a new moon, the moon provides

0

lux of illumination. The period of the lunar cycle is

29

53

days long. The moon will be full on December

25

2015

. Note that December

25

7

days before January

1

\newline

Find the formula of the trigonometric function that models the illumination

L

t

days after January

1

2016

. Define the function using radians.

\newline

L(t)=\square

Posted 4 months ago

Question

Valeria is playing with her accordion.

\newline

The length of the accordion

A(t)

\mathrm{cm}

) after she starts playing as a function of time

t

(in seconds) can be modeled by a sinusoidal expression of the form

a \cdot \cos (b \cdot t)+d

\newline

t=0

, when she starts playing, the accordion is

15 \mathrm{~cm}

long, which is the shortest it gets.

1

5

seconds later the accordion is at its average length of

21 \mathrm{~cm}

\newline

A(t)

\newline

t

should be in radians.

\newline

A(t)=\square

Posted 4 months ago

Question

After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly.

\newline

The population loses

\frac{1}{4}

of its size every

44

seconds. The number of remaining bacteria can be modeled by a function,

N

, which depends on the amount of time,

t

\newline

Before the medicine was introduced, there were

11

880

bacteria in the Petri dish.

\newline

Write a function that models the number of remaining bacteria

t

seconds since the medicine was introduced.

\newline

N(t)=\square

Posted 4 months ago