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Complet the T chart of values for the Exponential equation. Round to the nearest $10$ th if necessary. $\newline$ When you have checked your quiz and know that your T-Chart is correct, graph this Exponential equation and upload it (along with the others) to the Absolute Value and Exponential Graph Upload Assignment for points $\newline$ $y=3^{x}$ $\newline$ \begin{array}{c|c} $\newline$ x & y \\hline $\newline$ $0$ & (\newline\) $1$ & (\newline\) $2$ & (\newline\) $3$ & (\newline\) $-1$ & (\newline\) $-2$ & (\newline\)\end{array}

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Write exponential functions: word problems

Full solution

Q. Complet the T chart of values for the Exponential equation. Round to the nearest

10

th if necessary.

\newline

When you have checked your quiz and know that your T-Chart is correct, graph this Exponential equation and upload it (along with the others) to the Absolute Value and Exponential Graph Upload Assignment for points

\newline

y=3^{x}

\newline

\begin{array}{c|c}

\newline

x & y \\hline

\newline

0

& (\newline\)

1

& (\newline\)

2

& (\newline\)

3

& (\newline\)

-1

& (\newline\)

-2

& (\newline\)\end{array}

Substitute $x$ with $0$ : To find the value of $y$ when $x=0$ , we substitute $x$ with $0$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{0}$ $\newline$ Since any non-zero number raised to the power of $0$ is $1$ , we have: $\newline$ $0$ $0$
Substitute $x$ with $1$ : To find the value of $y$ when $x=1$ , we substitute $x$ with $1$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{1}$ $\newline$ Since any number raised to the power of $1$ is the number itself, we have: $\newline$ $y = 3$
Substitute $x$ with $2$ : To find the value of $y$ when $x=2$ , we substitute $x$ with $2$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{2}$ $\newline$ Calculating the power, we get: $\newline$ $y = 9$
Substitute $x$ with $3$ : To find the value of $y$ when $x=3$ , we substitute $x$ with $3$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{3}$ $\newline$ Calculating the power, we get: $\newline$ $y = 27$
Substitute $x$ with $-1$ : To find the value of $y$ when $x=-1$ , we substitute $x$ with $-1$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{-1}$ $\newline$ Since a negative exponent means taking the reciprocal of the base raised to the positive of that exponent, we have: $\newline$ $y = \frac{1}{3}$
Substitute $x$ with $-2$ : To find the value of $y$ when $x=-2$ , we substitute $x$ with $-2$ in the equation $y=3^{x}$ . $\newline$ $y = 3^{-2}$ $\newline$ Calculating the power, we get: $\newline$ $y = \frac{1}{9}$

More problems from Write exponential functions: word problems

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Each year, Francesca earns a salary that is

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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?

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Round your final answer to the nearest thousand.

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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.

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The half-life of the isotope beryllium-

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14

seconds. A sample of beryllium-

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was first measured to have

800

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Write an equation in terms of

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

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

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Rearrange the formula to highlight the measure in degrees Celsius.

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C=

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Question

2010

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\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

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\newline

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

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Question

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

45

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\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

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square kilometers?

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Give an exact answer expressed as a natural logarithm.

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

\newline

He finds that the relationship between the elapsed time

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, 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}

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

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

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Find the following trigonometric values.

\newline

Express your answers exactly.

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

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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

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\newline

L(t)=\square

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Question

Valeria is playing with her accordion.

\newline

The length of the accordion

A(t)

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) after she starts playing as a function of time

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\newline

t=0

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long, which is the shortest it gets.

1

5

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A(t)

\newline

t

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A(t)=\square

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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

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

N

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\newline

Before the medicine was introduced, there were

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880

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\newline

Write a function that models the number of remaining bacteria

t

seconds since the medicine was introduced.

\newline

N(t)=\square

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