The average rate of change of the function f(d) from d = 2 to d = 7 means that the radius of the algae specie increases by 0.1145 mm per day
The reasonable domain to plot the growth function
The function is given as:
f(d) = 11(1.01)^d
The domain is the number of days, the function can take
From the question, we have:
f(d) = 11.79 ---- maximum range
So, we have:
11(1.01)^d = 11.79
Divide both sides by 11
(1.01)^d = 1.07
Take the logarithm of both sides
d * log(1.01) = log(1.07)
Divide both sides by log(1.01)
d = 7
Hence, the reasonable domain of the function is 0 ≤ d ≤ 7
What the y-intercept represents?
We start by setting d to 0.
d = 0
So, we have:
f(0) = 11(1.01)^0
Evaluate
f(0) = 11
This means that the y-intercept implies that the initial radius of the algae specie is 11 mm
The average rate of change from d = 2 to d = 7
Calculate f(2) and f(7)
f(2) = 11(1.01)^2 = 11.2211
f(7) = 11(1.01)^7 = 11.7935
The average rate is then calculated as:
Rate = (f(7) - f(2))/(7 - 2)
This gives
Rate = (11.7935 - 11.2211)/(7 - 2)
Evaluate
Rate = 0.1145
Hence, the average rate of change of the function f(d) from d = 2 to d = 7 is 0.1145 and it means that the radius of the algae specie increases by 0.1145 mm per day
Read more about functions at:
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