f(x)=3.1�ã(x+19
1.Decribe the graph be obtained using transformations of the square root function.
First, vertically stretch the graph of f (x) = by the factor 3.1; then shift the results up 19 units.
2.Determine how to tell the model describes the actual height of a four year old girl.
40.5in
3. Use the model to find the average rate of change, in inches per month, between birth and 10 months.
It is 0.8 inches
4. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. compare with the answer 3.
0.2 inches it was more in from 0-10
10 x = 1000
To find the average rate of change between 50 and 60 months, we subtract the output values at those two points and divide it by the difference in months.
First, let's find the height at 50 months:
f(50) = 3.1√(50 + 19) = 3.1√69 ≈ 15.332 inches
Next, let's find the height at 60 months:
f(60) = 3.1√(60 + 19) = 3.1√79 ≈ 16.032 inches
Now, let's calculate the average rate of change:
Rate of change = (f(60) - f(50))/ (60 - 50)
= (16.032 - 15.332) / 10
= 0.7 / 10
= 0.07 inches per month
The average rate of change between 50 and 60 months is 0.07 inches per month. Comparing this with the previous answer of 0.2 inches per month for the range of 0-10 months, we can see that the rate of height change has decreased from 0-10 months to 50-60 months.