Question

Question 2
1 pts
Use Desmos to identify key features of the function y = 3 * (1.2) ^ x
Select all that are true.
The function is decreasing at a rate of 20%
The y-intercept is 0
The asymptote is at y = 3
The function is increasing at a rate of 20%
The asymptote is at y = 0
The y-intercept is 3

Answer 1

To analyze the function \( y = 3 \cdot (1.2)^x \), let's go through each of the provided statements:

1. **The function is decreasing at a rate of 20%**: This is false. Since the base \( 1.2 \) is greater than 1, the function is increasing, not decreasing.

2. **The y-intercept is 0**: This is false. The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the function:
\[
y = 3 \cdot (1.2)^0 = 3 \cdot 1 = 3
\]
So the y-intercept is \( 3 \).

3. **The asymptote is at y = 3**: This is false. The horizontal asymptote of an exponential function of this form is typically at \( y = 0 \).

4. **The function is increasing at a rate of 20%**: This is true. The base \( 1.2 \) means that for every unit increase in \( x \), the function increases by \( 20\% \) of its value.

5. **The asymptote is at y = 0**: This is true. As \( x \) approaches negative infinity, the function approaches \( y = 0 \).

6. **The y-intercept is 3**: This is true, as shown earlier.

Based on the analysis, the true statements are:

- The function is increasing at a rate of 20%.
- The asymptote is at \( y = 0 \).
- The y-intercept is 3.