Question

A population of deer is increasing exponentially. Which exponential equation in the form y=abx
represents the situation shown in the graph?
graph shows a line passing through the points (0,60), (1,90), and (2,135)


(1 point)
Responses

y=60(23)x
y is equal to 60 times 2 thirds to the x th power

y=90(3)x
y is equal to 90 times 3 to the x th power

y=60(32)x
y is equal to 60 times 3 halves to the x th power

y=90(52)x

Answer 1

To determine the correct exponential equation in the form \( y = ab^x \) based on the given points in the graph, we will analyze the provided points: (0, 60), (1, 90), and (2, 135).

1. From the point (0, 60), we know that when \( x = 0 \), \( y = a \). Therefore, \( a = 60 \).
\[
y = 60b^x
\]

2. We can use the other points to find \( b \). Let's use point (1, 90):
\[
90 = 60b^1
\]
Dividing both sides by 60 gives:
\[
b = \frac{90}{60} = \frac{3}{2}
\]

3. Now we can confirm \( b \) using point (2, 135):
\[
y = 60b^2
\]
Substituting \( b = \frac{3}{2} \):
\[
y = 60\left(\frac{3}{2}\right)^2 = 60 \times \frac{9}{4} = 135
\]
This matches the point (2, 135), validating our calculations.

Therefore, the exponential equation representing the population of deer is:
\[
y = 60\left(\frac{3}{2}\right)^x
\]

Thus, the correct answer is:
**y = 60(32)x** (y is equal to 60 times 3 halves to the x th power).