Chapter ISG, Problem 9.9.2.1P

a.

To determine

To find the function of tiles.

Answer to Problem 9.9.2.1P

Function of gray tiles

  $f(n)=n^2+4$

Function of white tiles

  $g(n)=4n$

Explanation of Solution

Given information:

Pattern of total number of tiles at stages: $9,\text{ 16, 25}\mathrm{...}$

Pattern of total number of gray tiles at stages: $5,\text{ 8, 13}\mathrm{.......}$

Pattern of total number of white tiles at stages: $4,\text{ 8, 12}\mathrm{.......}$

Calculation:

Pattern of total number of gray tiles at stages: $5,\text{ 8, 13}\mathrm{.......}$

Function of gray tiles

  $f(n)=n^2+4$

Pattern of total number of white tiles at stages: $4,\text{ 8, 12}\mathrm{.......}$

Function of white tiles

  $g(n)=4n$

n is number of tiles.

b.

To determine

To calculate height when parashutist release parachute.

Answer to Problem 9.9.2.1P

  $h(n)=n^2+4n+4$

  $h(10)=144$

Explanation of Solution

Given information:

Function of gray tiles

  $f(n)=n^2+4$

Function of white tiles

  $g(n)=4n$

Calculation:

Function of gray tiles

  $f(n)=n^2+4$

Function of white tiles

  $g(n)=4n$

Function of total number of tiles

  $h(n)=f(n)+g(n)$

Put value of function of gray and white tiles

  $h(n)=n^2+4+4n$

Then $h(n)=n^2+4n+4$

  $h(10)={10}^2+4(10)+4$

On solving,

  $h(10)=100+40+4$

On solving,

  $h(10)=144$

c.

To determine

To find how to know about stage 10 total number of tiles.

Answer to Problem 9.9.2.1P

  $f(12)=144$

Explanation of Solution

Given information:

Pattern of total number of tiles at stages: $9,\text{ 16, 25}\mathrm{...}$

  $h(10)=144$

Calculation:

Pattern of total number of tiles at stages: $9,\text{ 16, 25}\mathrm{...}$

Function

  $f(n)=n^2,3\le n$

At stage 10

  $n=12$

  $f(12)={12}^2$

On solving,

  $f(12)=144$