Question

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

Answer 1

Answer:

x     y

-2   7

-1    10.5

0    15.75

1     23.625

2    35.4375

Step-by-step 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 $b^{-1}=\frac{1}{b}$, so:

$10.5=\frac{15.75}{b}$

$10.5b=15.75$

$b=\frac{15.75}{10.5}$

$b=1.5$

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 $x=2$

$y=15.75(1.5)^x$

$y=15.75(1.5)^2$

$y=35.4375$