Mathematics Algebra

Problem 1
Question 1The determination of the median height can be arrived at by taking the functional value of f (48). The value x should be substituted for 48. This should look like follows:
F(48)= 3.1√(48)+19
=3.1(6.928)+19
=21.47+19
=40.5
Question 2
The calculation obtained above indicates a median height of 40.5 inches. However, the actual height is said to be 40.2 inches. The meaning of this analysis is that the model has overestimated the height by the difference of 40.5-40.2 which is 0.3 inches.
Question 3
It is appropriate to determine the height of the girl during birth, considered as month zero. Once this has been achieved, it is good to substitute 0 in place of x. The function looks like this:
F(0)=3.1√(0)+19
=0+19
=19
Once this has been achieved, it is possible to determine the height at the 10th month. In this case, you should substitute the value 10 for x. The function yields:
F(10)=3.1√(10)+19
=3.1(3.162)+19
=9.8+19
=28.8
Question 4
The determination of the average amount of change can be obtained accordingly. It calls for the calculation of the average change as through:
The average change in height= change in height/ change in age (years).
F(10)-f(0)/ 10-0 = 28.8-19/10
=9.8/10
=0.98
=equivalent to 1
From this calculation, it can be deduced that the average change from 0 to 10 months of birth is 1 inch on a monthly basis.
The next step should involve the determination of the height of girls at month 50. In this case, 50 should be substituted for x as shown in the function below:
F(50)=3.

1√(50)+19
=3.1(7.07)+19
=21.9+19
=40.9
Additionally, it is possible to determine the height at month 60. 60 should be substituted for x as shown in the function below:
F(60)=3.1√(60)+19
=3.1(7.74)+19
=24+19
=43
Once this has been established, the average amount of change can be calculated. This is the average between months 50 and 60. In this function:
F(60)=f(50)/(60-50)= 43-40.9/(10)
=2.1/10
=0.2
From this calculation, it shows that the average rate is 0.2 inches on a monthly basis. The average of 0.2 is smaller compared to that obtained from 0 to 10 months. This is indicated as shown in the graph as shown below:
Graph: Median heights between different months

From the graph, there is the illustration of median heights. There is a steeper curve for 0 to 10 months compared to 50 to 60 months.