The exponential function represented by the table is [tex]f(x)=0.8(2)^x[/tex]
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
When x = 0, f(x) = 0.8.
So, we have:
[tex]ab^0 = 0.8[/tex]
Evaluate the exponent
[tex]a \times 1 = 0.8[/tex]
Evaluate the product
[tex]a = 0.8[/tex]
When x = 1, f(x) = 1.6
So, we have:
[tex]ab^1 = 1.6[/tex]
Evaluate the exponent
[tex]ab = 1.6[/tex]
Substitute 0.8 for a
[tex]0.8b = 1.6[/tex]
Divide both sides by 0.8
[tex]b = 2[/tex]
So, we have:
[tex]a = 0.8[/tex] and [tex]b = 2[/tex]
Substitute these values in [tex]f(x) = ab^x[/tex]
[tex]f(x)=0.8(2)^x[/tex]
Hence, the exponential function represented by the table is [tex]f(x)=0.8(2)^x[/tex]
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