Question

Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship

Enter the correct answer in the box by replacing the values of a and b.

f(x) = a(b)^x

Answer 1

SOLUTION

TO DETERMINE

Another copy machine also has the ability to reduce image dimensions, but by a different percentage. This graph shows the results found when copying a design x times. Use the graph to write the equation modeling this relationship

Enter the correct answer in the box by replacing the values of a and b.

$\sf{f(x) = a \: ({b}^{x} )}$

EVALUATION

Here it is given that Another copy machine also has the ability to reduce image dimensions, but by a different percentage.

Now the it is given that

$\sf{f(x) = a \: ({b}^{x} )} \: \: - - - (1)$

From the graph we see that

When x = 0 , y = f(x) = 8

Which gives

f(0) = 8

$\sf{ \implies \: 8 = a \: ( {b}^{0} )}$

$\sf{ \implies \: 8 = a \: \times 1}$

$\sf{ \implies \: a = 8 }$

Again x = 1 , y = f(x) = 4

Which gives

f(1) = 4

$\sf{ \implies \: 4 = a \: ( {b}^{1} )}$

$\sf{ \implies \: 4 = ab \: }$

$\sf{ \implies \: ab = 4 \: }$

$\sf{ \implies \: 8b = 4 \: }$

$\sf{ \implies \: b = 0.5 \: }$

Thus the required relationship is obtained by putting the values of a and b in Equation 1

Hence the required relationship is

$\sf{f(x) = 8 \: ({0.5}^{x} )}$

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