Question

In 1950, Brian's dad recieved $20 for his tenth birthday. His mother deposited it into a bank account for him. Everyone forgot about the money and made no further deposits or withdrawls. The table shows the account balance for several years.

Elapse time in years	Balance in account
0	20
5	26.77
10	35.82
15	47.93
20	64.14
25	85.84
30	114.87

5A) Enter the info on your calculator. Look at the scatterplot. What type of function represents this curve?

5B)what is the equation of best fit? Round all values to the nearest hundreth

5C)Use your equation to estimate the balance in the account when Brian's dad turn 70

Please show work will rate if done all questions

Answer 1

A scatterplot of vthe given data is attached. The scatterplot resembles an arm of an upwards opening parabola, i.e. the graph of a quadratix function. Let this function be y = f(x) = a+bx+cx², where x is the no. of years since 1950, when Brian's dad was 10 years old, y is the amount in his account and a,b,c are arbitrary real numbers.

When x = 0, y = 20 so that a = 20. Then the required function is y = f(x) = 20+ bx+cx². Also, when x = 15, y = 47.93 so that 15a+225b = 47.93,,,(1), and y = 85.84 when x = 25 so that 25a+625b = 85.84…(2).

The augmented matrix of this linear system is A =

15	225	47.93
25	625	85.84

The RREF of A is

1	0	42569/15000
0	1	1787/75000

Hence b = 42569/15000 and c = 1787/75000. Thus, the required function is y = f(x) = 20+(42569/15000)x +(1787/75000)x² = 20+2.838x +0.024x² ( on rounding off to the nearest hundredth).

Brian’s dad was 10 years old in 1950 (i.e. when x = 0) so that x = 60 when Brian's dad turns 70. Then the balance in his account is 20+2.838(60)+0.024(60)² = 20+170.28+86.4 = $ 276.68.