The graph models projected populations, in thousand, of two towns after x years. Both towns experience a 1.9% annual growth rate. Which equation represents g(x) as a translation of f(x)?

The image of the graph is missing, so i have attached it.

g(x) = 5/3 * f(x)

Step-by-step explanation:

We want to find the equation represents g(x) as a translation of f(x).

From the graph, the y = f(x) function curve has the following observations,

- At x = 0, y = f(0) = 30

- At x = 10, y = f(10) = 36

Similarly, from the graph, the y = g(x) function curve has the following observations,

- At x = 0, y = g(0) = 50

- At x = 10, y = g(10) = 60

From those coordinates on the graph, we can see that;

f(0) = 30 and g(0) = 50

It means that for us to make g(x) as a translation of f(x), g(0) = fraction * f(0)

Fraction = g(0)/f(0) = 50/30 = 5/3

Thus;

g(x) = 5/3 * f(x)

Let's confirm with the second coordinate;

Thus;

g(10) = 5/3 * f(10)

g(10) = 5/3 * 36

g(10) = 60

This value is same as what is on graph, thus we can conclude that;

The equation represents g(x) as a translation of f(x) is; g(x) = 5/3 * f(x)

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step-by-step explanation:

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step-by-step explanation:

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