Answer :
The 2-unit growth factor for f is 0.2304.
The 1-unit growth factor for f is 0.48.
The initial value of f is 57.
Given an exponential function f(x) = 57(0.48).
Formula for the exponential function is:
f(x) = a*b*x
Here, a= initial value, b = growth factor, x = variable.
The growth factor b can be calculated as 0.48.
In order to calculate the 2-unit growth factor, substitute (x + 2) in the given function. So the function becomes:
f(x+2) = 57(0.48)2
Now the growth factor is calculated using the formula, f(x+2)/f(x).
So the 2-unit growth factor is = 0.48^2 = 0.2304.
Now in order to calculate the 1-unit growth factor, substitute (x + 1) in the given function.
So the function becomes f(x+1) = 57(0.48)
Now the growth factor is calculated using the formula, f(x+1)/f(x).
So the 1-unit growth factor = 0.48.
From the given function, initial value a is 57. Hence the initial value of f is 57.
Therefore, the initial value of f is 57, the growth factors for 2-unit and 1-unit increases are 0.2304 and 0.48 respectively.
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