Answer:
The equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].
Step-by-step explanation:
The exponential growth function is represented by the expression described below:
[tex]y = a\cdot b^{x}[/tex] (1)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]a[/tex] - Initial value of [tex]y[/tex].
[tex]b[/tex] - Base.
By deriving (1), we obtain an expression for the slope of the curve:
[tex]y' = a\cdot b^{x} \cdot \ln b[/tex] (2)
If we know that [tex]x = 0[/tex], [tex]y = 3[/tex] and [tex]y' = 6[/tex], then we have the following system of equations:
[tex]a = 3[/tex] (3)
[tex]a\cdot \ln b = 6[/tex] (4)
By (3) in (4):
[tex]3\cdot \ln b = 6[/tex]
[tex]\ln b = 2[/tex]
[tex]b = e^{2}[/tex]
[tex]b = 7.389[/tex]
Therefore, the equation of curve is [tex]y = 3\cdot 7.389^{x}[/tex].
