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Find the missing values for the exponential function represented by the table below.

x y
-2 7
-1 10.5
0 15.75
1
2

1 Answer

4 votes

Answer:

x y

-2 7

-1 10.5

0 15.75

1 23.625

2 35.4375

Explanation:

The general equation of the exponential function is
y=ab^x.

We know from our table that when
x=0,
y=15.75. Let's replace those values in our equation:


y=ab^x


15.75=ab^0

Remember that
b^0=1, so:


15.75=a(1)


15.75=a


a=15.75

We also know from our table that when
x=-1,
y=10.5. Let's replace the values again:


y=ab^x


10.5=ab^(-1)

But we now know that
a=15.75, so let's replace that value as well:


10.5=15.75b^(-1)

Remember that
b^(-1)=(1)/(b), so:


10.5=(15.75)/(b)


10.5b=15.75


b=(15.75)/(10.5)


b=1.5

Now, we can put it all together to complete our exponential function:


y=ab^x


y=15.75(1.5)^x

To find the missing values, we just need to evaluate our function at
x=1 and
x=2:

- For
x=1


y=15.75(1.5)^x


y=15.75(1.5)^1


y=23.625

- For
x=2


y=15.75(1.5)^x


y=15.75(1.5)^2


y=35.4375

User Pulkit Jha
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