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The exponential function h, whose graph is given below, can be written as
h(x) = a.b².
5 4 3 2
Complete the equation for h(x).
h(x) =
Y
8.
7++
6+
40
3
2--
​

The Exponential Function H Whose Graph Is Given Below Can Be Written Ashx Ab5 4 3 2Complete The Equation For Hxhx Y8764032 class=

Sagot :

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]

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