Chapter ISG, Problem 4.2.3P

a.

To determine

To form an equation and to calculate how money he has when he turns 16.

Answer to Problem 4.2.3P

Equation for the given situation is $y-4000=200(x-10)$ .

He will have $5200 when he turns 16.

Explanation of Solution

Given information:

S’s uncle adds $200 in his account, on his birthday each year.

When he was 10 he had $4000 in his account.

Formula Used:

Equation of line is,

  $y-y1=m(x-x1)$

Calculation:

Since, every year he has $200 more in his account. Hence, slope is,

  $m=200$

When he was 10 he has $4000 in his account. Hence, a point is,

  $(10,4000)$

Substituting the values in the equation of line,

  $y-4000=200(x-10)$ _____________________(1)

For money S will have when he turns 16. Substituting the values in equation (1)

  $y-4000=200(16-10)$

On solving,

  $y-4000=1200$

Shifting left-hand side values to right-hand side,

  $y=1200+4000$

On solving,

  $y=5200$

Hence, he will have $5200 when he turns 16.

Conclusion:

Equation for the given situation is $y-4000=200(x-10)$ .

He will have $5200 when he turns 16.

b.

To determine

To calculate the initial deposit of S’s uncle.

Answer to Problem 4.2.3P

Initial deposit is $2000

Explanation of Solution

Given information:

Equation for S’s uncle’s deposit is,

  $y-4000=200(x-10)$ .

Formula Used:

Equation of line is,

  $y=mx+c$

Calculation:

Converting the line in the form of equation of line in terms of slope and intercept.

Opening the brackets,

  $y-4000=200x-2000$

Shifting left hand side variables to right hand side,

  $y=200x-2000+4000$

On solving,

  $y=200x+2000$

Hence, y- intercept is 2000.

Since, y-intersect shows the initial value of the function, that is, value of y when x is zero. Therefore, his uncle’s initial deposit is $2000.

Conclusion:His uncle’s initial deposit is $2000