Answer:
The exponential model is [tex]y = 0.07\cdot e^{0.73\cdot x}[/tex].
Step-by-step explanation:
The exponential model can be modelled by the following mathematical expression:
[tex]y = A\cdot e^{B\cdot x}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]A, B[/tex] - Coefficients.
If we know that [tex](x_{1}, y_{1}) = (7,12)[/tex] and [tex](x_{2}, y_{2}) = (8,25)[/tex], then we get the following system of equations:
[tex]A\cdot e^{7\cdot B} = 12[/tex] (2)
[tex]A\cdot e^{8\cdot B} = 25[/tex] (3)
If we divide (3) by (2), we calculate the value of [tex]B[/tex]:
[tex]e^{B}=\frac{25}{12}[/tex]
[tex]B = \ln \frac{25}{12}[/tex]
[tex]B \approx 0.734[/tex]
And by (2), we determine the value of [tex]A[/tex]:
[tex]A = 12\cdot e^{-7\cdot B}[/tex]
[tex]A = 0.0704[/tex]
The exponential model is [tex]y = 0.07\cdot e^{0.73\cdot x}[/tex].
