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Answer:
a)
initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
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[tex]e^{rt}[/tex]
so,
at S₀ = 1 million dollars } { r = 0.10 }
S(t) = 1.[tex]e^{0.10t}[/tex]
Therefore, initial value problem representing the salary is; S(t) = 1.[tex]e^{0.10t}[/tex]
b) What is s(0) and s(1)
at s(0)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(0) = 1.[tex]e^{0.10*0}[/tex]
S(0) = 1.[tex]e^{0}[/tex]
S(0) = 1
Therefore; S(0) is 1 million dollar
at s(1)
S(t) = 1.[tex]e^{0.10t}[/tex]
we substitute
S(1) = 1.[tex]e^{0.10*1}[/tex]
S(1) = 1.[tex]e^{0.10}[/tex]
S(1) = [tex]e^{0.10}[/tex]
S(1) = 1.105170918075647
Therefore; S(1) is 1.105170918075647 million dollar