Determine if the equation y = 2^x represents exponential growth or decay
I thought at first it was growth but now I think it might be decay because there is no "b" in a parentheses so do I assume b is less than 1 so it's decay?
Please help
What happens if x > 1? What happens if x is negative or a fraction?
What does "b" have to do with this problem?
A BALL REBOUNDS ONE-HALF THE DISTANCE THAT IT FALLS. IF THE BALL IS DROOPED FROM A HEIGHT OF 512 FEET,HOW HIGH DOES IT GO ON ITS EIGHT REBOUND.
f(x)=14−0.5xf, left parenthesis, x, right parenthesis, equals, 14, minus, 0, point, 5, x
f(30)=f(30)=f 30
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To determine whether the equation y = 2^x represents exponential growth or decay, we need to consider the value of the base, which is 2 in this case.
In general, if the base of an exponential function is greater than 1, it indicates exponential growth. Conversely, if the base is between 0 and 1, it represents exponential decay.
Since the base in the given equation, y = 2^x, is 2, which is greater than 1, it means that the function represents exponential growth. Therefore, the equation y = 2^x represents exponential growth rather than decay.
To summarize, when determining whether an exponential function represents growth or decay:
- If the base is greater than 1, it represents exponential growth.
- If the base is between 0 and 1, it represents exponential decay.