Solution:
The volume of the cases in 2001 is given below as
[tex]=17.8billion[/tex]
The percentage increase from 2000 is given below as
[tex]=4\%[/tex]
The exponential function is given below as
[tex]\begin{gathered} y=ab^t \\ where, \\ b=1+r \\ r=4\% \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} y=ab^{t} \\ 17.8=a(1+\frac{4}{100})^1 \\ 1.04a=17.8 \\ \frac{1.04a}{1.04}=\frac{17.8}{1.04} \\ a=17.12billion \end{gathered}[/tex]
Hence,
The final answer is YES, THE EXPONENTIAL MODEL FUNCTION IS APPROPRIATE
Therefore,
The exponential model after y years will be
[tex]C(y)=17.12(1.04)^y\text{ }billion\text{ }cases[/tex]
