Question

Zena planted a bamboo stalk in her backyard. The height of the plant increased in height over the next few months. Which exponential equation in the form y=abxy=abx represents the situation shown on the graph?
Graph
(2,6.75)
(1,4.5)
(0,3)<starting point
(1 point) Responses y=4.5(3)xy=4.5(3)xy is equal to 4 point 5 times 3 to the x th power y=3(23)xy=3(23)xy is equal to 3 times 2 thirds to the x th power y=3(32)xy=3(32)xy is equal to 3 times 3 halves to the x th power y=4.5(52)x

Answer 1

To determine the correct exponential equation in the form \( y = ab^x \), we need to analyze the given points from the graph.

1. Starting point (0, 3): This indicates that when \( x = 0 \), \( y = 3 \). Therefore, \( a = 3 \).
2. Next point (1, 4.5): When \( x = 1 \), \( y = 4.5 \). Using the equation \( y = ab^x \):
- \( 4.5 = 3b^1 \)
- \( b = \frac{4.5}{3} = 1.5 \).

3. To find the equation, we have:
\[
y = 3(1.5)^x
\]

Now, let's verify the equation with the points given:
- For \( x = 2 \):
- \( y = 3(1.5)^2 = 3 \cdot 2.25 = 6.75 \), which matches the point (2, 6.75).

So the equation \( y = 3(1.5)^x \) fits the points provided. We don't have 1.5 in any of the options, but we can also notice from our calculations that since 1.5 can also be written as \( \frac{3}{2} \), if we substitute \( 1.5 \) as \( \frac{3}{2} \), we have \( y = 3\left(\frac{3}{2}\right)^x \).

Given the available choices, the closest option that matches our derived equation format is:

**None exactly match, but based on the structure, the option**
\( y = 3\left(\frac{3}{2}\right)^x \) (which is conceptually equivalent to the option mentioning fractions).

Please ensure that in context, we may need to check the available options again to pick the closest one based on the exponentiation scheme and provided points.