Chapter 7 - Exponential and Logarithmic Functions - 7-1 Exploring Exponential Models - Lesson Check: 2

The function represents exponential growth and the y-intercept is at $(0,0.75)$.

Work Step by Step

In order to determine whether this graph represents exponential growth or exponential decay, we must first remember that exponential growth and decay functions look like this: $y=a(b)^x$ $a$ = y-intercept $b$ = Rate of growth/decay If $b$ is between 0 up to but not including 1, the function is exponential decay. If $b$ is greater than 1, the function is exponential growth. In this case, $b = 4$, which is greater than $1$, so the function represents exponential growth. To find the y-intercept, we plug in $0$ for $x$. $y = 0.75(4)^0 = 0.75(1) = 0.75$ The y-intercept is $(0, 0.75)$

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