Question

An incomplete table of values for an exponential function is shown. The exponential function is of the form y=a\cdot b^x where a is a real number such that a\ne0 and b is a positive real number not equal to 1.

Enter the values of a and b in the boxes given below, then complete the table with possible values for the exponential function.

X- 0-1-2-3
Y-96------

Answer 1

Answer:

−3−99

because if

+0−1−2−3−96

x+0−1−2−3−96

−99−3

Answer 2

The required exponential function will be $f(x) =9(\frac{2}{3} )^x$ with a and b values 9 and 2/3 respectively.

The given exponential function is:

$f(x) = ab^x$

What is a function?

A function is a rule that relates two variables.

Point (0,9) lies on the graph of the given function.

So, $9=ab^0$

$a=9$

So, f(x) becomes $f(x)=9b^x$

Point (1,6) also lies on the graph of the given function.

So, $6=9b$

$b=\frac{2}{3}$

So, the required function will be $f(x) =9(\frac{2}{3} )^x$

Therefore, The required exponential function will be $f(x) =9(\frac{2}{3} )^x$ with a and b values 9 and 2/3 respectively.

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