The reasonable domain to plot the function is 0 < d <= 1.4, the y-intercept of the function is 7 and the average rate of change from d = 4 to d = 11 is 0.64
The reasonable domain to plot the function?
The function is given as:
f(d) = 7(1.06)^d
The maximum radius is 13.29.
So, we have:
7(1.06)^d = 13.29
Divide both sides by 7
(1.06)^d = 1.90
Take the logarithm of both sides
dlog(1.60) = log(1.90)
Divide both sides by log(1.60)
d = 1.4
Hence, the reasonable domain to plot the function is 0 < d <= 1.4
The y-intercept of the function
This is when d = 0.
So, we have:
f(0) = 7(1.06)^0
Evaluate
f(0) = 7
Hence, the y-intercept of the function is 7
The average rate of change
From d = 4 to d = 11
Calculate f(4) and f(11)
f(4) = 7(1.06)^4 = 8.84
f(11) = 7(1.06)^11 = 13.29
The average rate of change is
Rate = (13.29 - 8.84)/(11 - 4)
Rate = 0.64
Hence, the average rate of change from d = 4 to d = 11 is 0.64
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