Question

an exponential function has these characteristics:
-the y-intercept is 2
-the function increases at a rate of 50%
which graph best re[resents this function?

Answer 1

To find the correct graph for the given exponential function, we can use the information provided:

1. **Y-intercept is 2**: This means that when \( x = 0 \), \( y = f(0) = 2 \).
2. **The function increases at a rate of 50%**: This indicates that the growth rate is 50%. In exponential terms, this means that the function can be written in the form:
\[
f(x) = a(1 + r)^x
\]
where \( r = 0.5 \) (representing a 50% increase), and \( a \) is the initial value (the y-intercept). Thus:

\[
f(x) = 2(1 + 0.5)^x = 2(1.5)^x
\]

Now, the general equation for our exponential function is:
\[
f(x) = 2(1.5)^x
\]

To find the proper graph:
- At \( x = 0 \), \( f(0) = 2(1.5)^0 = 2 \).
- The function will increase rapidly due to the 50% growth rate. As \( x \) increases, \( f(x) \) will quickly move away from the y-intercept.

By looking for the graph that intersects at (0,2) and demonstrates rapid exponential growth, you can identify the correct one.

If you have options or specific graphs to compare, you can identify the one that meets these criteria.