Suppose that a football coach gets a salary of one million dollars now, and a raise of 10% every year (so exponential growth model). Let s be the salary in millions of dollars, and t is time in years. (a) Write an initial value problem to represent the salary s. Label 0.2.14 (modified) (b) What is s(0) and s(1)

a)

initial value problem representing the salary is; S(t) = 1.  

b)

S(0) = 1

Therefore; S(0)  is 1 million dollar

S(1) = 1.105170918075647

Therefore; S(1)  is 1.105170918075647 million dollar

Step-by-step explanation:

Given that;

Initial salary of football coach = 1 million dollar

raise of 10% every year (so exponential growth model) r = 10% = 0.10

a) initial value problem to represent the salary

lets S represent salary in millions dollars and t represent time in years.

S(t) = S₀

so,

at S₀ = 1 million dollars } { r = 0.10 }

S(t) = 1.  

Therefore, initial value problem representing the salary is; S(t) = 1.  

b) What is s(0) and s(1)

at s(0)

S(t) = 1.  

we substitute

S(0) = 1.

S(0) = 1.

S(0) = 1

Therefore; S(0)  is 1 million dollar

at s(1)

S(t) = 1.  

we substitute

S(1) = 1.

S(1) = 1.

S(1) =

S(1) = 1.105170918075647

Therefore; S(1)  is 1.105170918075647 million dollar

the first one, all those points on the line just make a strait line.