9. Does the function represent exponential growth or
exponential decay? Identify the growth or decay
factor.
= 9 ∙ (1/2)ˣ
the quantity being raised to a power is less than one ... this is decay
Thank you so much scott!!
Well, it looks like we have a case of exponential decay here. The growth or decay factor is 1/2. Just like that leftover burrito in the fridge, it keeps getting smaller and smaller each time!
To determine whether the function represents exponential growth or decay, we need to examine the base of the exponent in the function.
In this case, the base of the exponent is 1/2. If the base is greater than 1, the function represents exponential growth. If the base is between 0 and 1, the function represents exponential decay.
Here, the base 1/2 is less than 1, so the function represents exponential decay.
To identify the growth or decay factor, we look at the coefficient of the function, which is 9. In exponential decay, the growth factor is always less than 1. Therefore, the decay factor is 1/2.
In summary, the function = 9 ∙ (1/2)ˣ represents exponential decay with a decay factor of 1/2.