Question
Points on graph
(0,3), (1,4.5)
What is the correct exponential equation
(0,3), (1,4.5)
What is the correct exponential equation
Answers
GPT-4o mini
To find the exponential equation of the form \( y = ab^x \) that passes through the points \( (0, 3) \) and \( (1, 4.5) \), we can use these points to find the values of \( a \) and \( b \).
1. **Using the first point \( (0, 3) \)**:
\[
y = ab^0 \implies y = a \implies 3 = a
\]
2. **Using the second point \( (1, 4.5) \)**:
\[
y = ab^1 \implies y = ab \implies 4.5 = 3b
\]
To solve for \( b \):
\[
b = \frac{4.5}{3} = 1.5
\]
Now that we have \( a \) and \( b \), we can substitute these values into the exponential function:
\[
y = 3(1.5)^x
\]
Thus, the exponential equation that fits the given points is:
\[
y = 3(1.5)^x
\]
1. **Using the first point \( (0, 3) \)**:
\[
y = ab^0 \implies y = a \implies 3 = a
\]
2. **Using the second point \( (1, 4.5) \)**:
\[
y = ab^1 \implies y = ab \implies 4.5 = 3b
\]
To solve for \( b \):
\[
b = \frac{4.5}{3} = 1.5
\]
Now that we have \( a \) and \( b \), we can substitute these values into the exponential function:
\[
y = 3(1.5)^x
\]
Thus, the exponential equation that fits the given points is:
\[
y = 3(1.5)^x
\]