Question

A population of deer is increasing exponentially. Which exponential equation in the form y=abx
represents the situation shown in the graph?



(1 point)
Responses

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

y=90(52)x
y is equal to 90 times 5 halves to the x th power

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

y=90(3)x

Answer 1

To determine which exponential equation represents the given situation, we need to interpret the options in terms of the typical exponential growth form \( y = ab^x \), where \( a \) is the initial value and \( b \) is the growth factor.

Let's briefly analyze the options:

1. **\( y = 60(32)^x \)**: This indicates a growth factor of \( 32 \), which suggests very rapid growth.

2. **\( y = 90(52)^x \)**: This indicates a growth factor of \( 52 \), which also suggests very rapid growth.

3. **\( y = 60(23)^x \)**: This indicates a growth factor of \( \frac{2}{3} \) (or approximately \( 0.67 \)), suggesting decline rather than growth.

4. **\( y = 90(3)^x \)**: This indicates a growth factor of \( 3 \), which suggests exponential growth at a reasonable rate.

Considering that the population of deer is increasing exponentially, we would look for a growth factor greater than \( 1 \).

Both the first and second options suggest extremely high growth factors, while the third indicates decline. The fourth option suggests a reasonable exponential growth with a factor of \( 3 \).

Since we want to confirm the rapid growth of a deer population, the appropriate choice from the provided options would be **\( y = 90(3)^x \)**, which signifies exponential growth.