What is the exponential growth or decay. Of this function and the constant percentage?
20(.876)^x
Would the percentage be expressed a decimal? I know it is decay ,so would you just add a negative to whatever percentage you get?
it's decay; because the base, being raised to a power, is less than one
the percentage is the difference between the base and one
.876 - 1 = -.124 = -12.4%
To determine whether a function represents exponential growth or decay, we need to look at the base of the function. In this case, the base of the function is (0.876)^x.
If the base (0.876) is greater than 1, then the function represents exponential growth.
If the base is between 0 and 1, then the function represents exponential decay.
Since the base in this case is less than 1 (0.876), the function represents exponential decay.
To find the constant percentage of decay, we subtract the base from 1 and multiply by 100 to get a percentage. So, the constant percentage of decay in this case is (1 - 0.876) * 100 = 0.124 * 100 = 12.4%.
To express this percentage as a decimal, we divide it by 100: 12.4% / 100 = 0.124. Thus, the decimal representation of the decay rate for this function is 0.124.
If you wish to express the decay rate as a negative value, you can add a negative sign to the percentage or the decimal value. So, the decay rate can be either -12.4% or -0.124, representing the same concept of decay.