Question

which statement about the graph of y=16(0.5)^x is not true?
a the y-intercept is (0,16)
b the graph is decreasing for all values of x
c the x-intercept is (0.5,0)
d the graph has a horizontal asymptote of y=0

Answer 1

To analyze the function \( y = 16(0.5)^x \) and determine which statement is not true, let's examine each option:

a. **The y-intercept is (0, 16)**:
- To find the y-intercept, we substitute \( x = 0 \):
\[
y = 16(0.5)^0 = 16 \cdot 1 = 16
\]
So, the y-intercept is (0, 16). This statement is true.

b. **The graph is decreasing for all values of x**:
- The base of the exponential function, \( 0.5 \), is between 0 and 1, which means the function is indeed decreasing as \( x \) increases. This statement is true.

c. **The x-intercept is (0.5, 0)**:
- To find the x-intercept, we set \( y = 0 \) and solve for \( x \):
\[
0 = 16(0.5)^x
\]
However, \( 16(0.5)^x \) cannot equal 0 for any real value of \( x \) because \( (0.5)^x \) is always positive. Therefore, there is no x-intercept. This statement is false.

d. **The graph has a horizontal asymptote of y = 0**:
- As \( x \) approaches infinity, \( (0.5)^x \) approaches 0, and thus \( y \) approaches 0. Therefore, the graph does have a horizontal asymptote at \( y = 0 \). This statement is true.

Thus, the statement that is not true is:
**c. The x-intercept is (0.5, 0)**.