Answer:
as shown in the attached file
Step-by-step explanation:
The detailed steps and application of differential equation, the use of integrating factor to generate the solution and to solve for the initial value problem is as shown in the attached file.
The geometric sequence that shows the height of the fourth bounce in bold is B) 9, 8.1, 7.3, 6.6,...
So, let's make these two values improper fractions so they're easier to work with. 
So, to get the rate he grew in those months we have:
And to get the rate he grew in one month we have to divide both our numerator and our denominator by 21 to get:
aka he grew 1.24 inches in a month.