Answer:
[tex]y=(0.2)4^x[/tex]
Step-by-step explanation:
General form of the exponential function: [tex]y=ab^x[/tex]
Substituting the first point (0, 0.2) into the function:
[tex]\implies 0.2=ab^0[/tex]
As any number to the zero power always gives one, [tex]b^0=1[/tex]
[tex]\implies0.2=a \times 1[/tex]
[tex]\implies a=0.2[/tex]
Therefore, [tex]y=(0.2)b^x[/tex]
Substituting the second point (1, 1.8) into the function:
[tex]\implies0.8=(0.2)b^1[/tex]
[tex]\implies0.8=(0.2)b[/tex]
[tex]\implies b=\frac{0.8}{0.2}[/tex]
[tex]\implies b=4[/tex]
So the final exponential equation is:
[tex]y=(0.2)4^x[/tex]
Checking the equation with the remaining two points:
[tex]x=2 \implies (0.2)4^2=3.2 \ \ \ \checkmark[/tex]
[tex]x=3 \implies (0.2)4^3=12.8 \ \ \ \checkmark[/tex]
