(FAN AND MEDAL) help please!
A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after n days:
f(n) = 8(1.05)n
Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(n) represent? (2 points)
Part C: What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent? (4 points)
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Domain will be talking about the values of n.
Now when we solve for f(n) = 11.26 we get 7.005... so a reasonable range to plot the graph would be from n = 0 to 8
The y-intercept is the point where n = 0. But n represents the number of days, i.e. time elapsed. So at n = 0 the point represents the initial reading.
At n = 2, f(2) = 8*(1.05)^2 = 8.82
At n = 6, f(6) = 8*(1.05)^6 = 10.72
The average rate of change is (change in height)/(change in n)
The change in height is 10.72 - 8.82 = 1.9
The change in n is 6 - 2 = 4
So the average rate of change is 1.9/4 = 0.475
But what is the average rate of change? It is the average daily (because a single change in n corresponds to a day) growth of the plant (because f(n) represents height)
thats the answers?
yes, i just ant to make sure, because this work value 30 pts