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Decide whether the word problem represents a linear or exponential function. Circle either linear or exponential. Then, write the function formula.

Decide whether the word problem represents a linear or exponential function. Circle-example-1
User Ranny
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a. The given table is

Notice, the value of x increases at equal intervals of 1

Also, the value of y increases at an equal interval of 3

This means for the y values the difference between consecutive terms is 3

Also, for the x values, the difference between consecutive terms is 1

Hence, the table represents a linear function

The general form of a linear function is


y=mx+c

Where m is the slope

From the interval increase


m=(\Delta y)/(\Delta x)=(3)/(1)=3

Hence, m = 3

The equation becomes


y=3x+c

To get c, consider the values

x = 0 and y = 2

Thi implies


\begin{gathered} 2=3(0)+c \\ c=2 \end{gathered}

Hence, the equation of the linear function is


y=3x+2

b. The given table is

Following the same procedure as in (a), it can be seen that there is no constant increase in the values of y

Hence, the function is not linear

This implies that the function is exponential

The general form of an exponential function is given as


y=a\cdot b^x

Consider the values

x =0, y = 3

Substitute x = 0, y = 3 into the equation

This gives


\begin{gathered} 3=a* b^0 \\ \Rightarrow a=3 \end{gathered}

The equation become


y=3\cdot b^x

Consider the values

x =1, y = 6

Substitute x = 1, y = 6 into the equation

This gives


\begin{gathered} 6=3\cdot b^1 \\ \Rightarrow b=(6)/(3)=2 \end{gathered}

Therefore the equation of the exponential function is


y=3\cdot2^x

c. The given table is

As with (b) above,

The function is exponential

Using


y=a\cdot b^x

When

x = 0, y = 10

This implies


\begin{gathered} 10=a\cdot b^0 \\ \Rightarrow a=10 \end{gathered}

The equation becomes


y=10\cdot b^x

Also, when

x = 1, y =5

The equation becomes


\begin{gathered} 5=10\cdot b^1 \\ \Rightarrow b=(5)/(10) \\ b=(1)/(2) \end{gathered}

Therefore, the equation of the exponential function is


y=10\cdot((1)/(2))^x

Decide whether the word problem represents a linear or exponential function. Circle-example-1
Decide whether the word problem represents a linear or exponential function. Circle-example-2
Decide whether the word problem represents a linear or exponential function. Circle-example-3
User Luke Melia
by
7.6k points

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