Answer:
[tex]\bf\displaystyle h(x)=4\left(\frac{1}{2} \right)^x[/tex]
Step-by-step explanation:
We can find the exponential function h(x) by substituting the [tex]x[/tex] and [tex]y[/tex] with any 2 points from the graph (since the function has 2 variables: [tex]a[/tex] and [tex]b[/tex])
Given:
- [tex](x_1,y_1)[/tex] = (0, 4)
- [tex](x_2,y_2)[/tex] = (1, 2)
Then:
[tex]h(x)=a\cdot b^x[/tex]
[tex]y_1=a\cdot b^{x_1}[/tex]
[tex]4=a\cdot b^0[/tex]
[tex]4=a\cdot 1[/tex]
[tex]\bf a=4[/tex]
[tex]y_2=a\cdot b^{x_2}[/tex]
[tex]2=4\cdot b^1[/tex]
[tex]b=2\div4[/tex]
[tex]\displaystyle\bf b=\frac{1}{2}[/tex]
Now, substitute the values of [tex]a[/tex] and [tex]b[/tex] to the function:
[tex]h(x)=a\cdot b^x[/tex]
[tex]\bf\displaystyle h(x)=4\left(\frac{1}{2} \right)^x[/tex]
