Question

Points
(0,30000), (1,22500)
What is the correct exponential equation

Answer 1

To find the exponential equation that fits the given points \((0, 30000)\) and \((1, 22500)\), we can use the general form of an exponential function:

\[
y = ab^x
\]

Here, \(a\) is the initial value (the value of \(y\) when \(x = 0\)) and \(b\) is the base of the exponent.

From the point \((0, 30000)\), we can determine that:

\[
a = 30000
\]

Now we can plug in the second point \((1, 22500)\) into the equation to find \(b\):

\[
22500 = 30000b^1
\]

Now, solve for \(b\):

\[
b = \frac{22500}{30000} = \frac{15}{20} = \frac{3}{4}
\]

So, the values of \(a\) and \(b\) are:

\[
a = 30000, \quad b = \frac{3}{4}
\]

Putting it all together, the exponential equation that fits the points \((0, 30000)\) and \((1, 22500)\) is:

\[
y = 30000 \left(\frac{3}{4}\right)^x
\]