Question

Points on a graph
(0,4), (1,7.6), (2,14.44)
Use the graph to fill in the missing elements of the exponential growth equation
y = __(__)^x

Answer 1

To find the parameters of the exponential growth equation \( y = a(b)^x \), we need to determine the values of \( a \) and \( b \) using the points provided: (0, 4), (1, 7.6), and (2, 14.44).

From the point (0, 4):

\[
y = a(b)^0 = a(1) = a
\]

Thus, \( a = 4 \).

Next, we can use the other points to find \( b \). We can set up equations using the remaining points.

Using the point (1, 7.6):

\[
y = a(b)^1
\]
Substituting in \( a \):

\[
7.6 = 4(b)
\]
Solving for \( b \):

\[
b = \frac{7.6}{4} = 1.9
\]

Now we can use point (2, 14.44) to check our work:

\[
y = a(b)^2
\]
Substituting \( a \) and \( b \):

\[
14.44 = 4(1.9)^2
\]

Calculating \( (1.9)^2 \):

\[
1.9^2 = 3.61
\]

Now calculate \( 4(3.61) \):

\[
4 \times 3.61 = 14.44
\]

This matches the point (2, 14.44), confirming that our values are correct.

Thus, the exponential growth equation is:

\[
y = 4(1.9)^x
\]