Question

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)

Answer 1

a)

initial value problem representing the salary is; S(t) = 1.
`e^(0.10t)`

b)

S(0) = 1

Therefore; S(0) is 1 million dollar

S(1) = 1.105170918075647

Therefore; S(1) is 1.105170918075647 million dollar

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
`e^(rt)`

so,

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

S(t) = 1.
`e^(0.10t)`

Therefore, initial value problem representing the salary is; S(t) = 1.
`e^(0.10t)`

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

at s(0)

S(t) = 1.
`e^(0.10t)`

we substitute

S(0) = 1.
`e^(0.10*0)`

S(0) = 1.
`e^(0)`

S(0) = 1

Therefore; S(0) is 1 million dollar

at s(1)

S(t) = 1.
`e^(0.10t)`

we substitute

S(1) = 1.
`e^(0.10*1)`

S(1) = 1.
`e^(0.10)`

S(1) =
`e^(0.10)`

S(1) = 1.105170918075647

Therefore; S(1) is 1.105170918075647 million dollar