Tell whether exponential growth, decay, or neither.
1. y = -2^{x-1} -4 (by looking at formula)
ans: decay because b = -2
Identity the range of the function
1. y = -7(3/2)^x + 4 (by looking at formula)
ans: range is y>4 because +4 is asymptote?
#1. if |b| > 1 it's growth
this graph is just reflected
for the range, you missed the leading "-" sign. The range is y < 4
Thank you.
To determine whether a function exhibits exponential growth, decay, or neither, we need to examine the value of the base (b) in the exponential equation.
In the first example, the equation is y = -2^(x-1) - 4. By looking at the formula, we can see that the base (b) is -2. Since the base is negative, this indicates decay. Therefore, the function is exhibiting exponential decay.
For the second example, the equation is y = -7(3/2)^x + 4. By looking at the formula, we can see that the base (b) is 3/2, which is positive. In this case, positive b values indicate exponential growth. However, it's important to note that the given equation also includes a constant term of +4. This constant does not affect the growth/decay nature of the function but shifts the entire graph upwards by 4 units.
Moving on to identifying the range of a function, in this case, y = -7(3/2)^x + 4. To determine the range, we need to find the set of all possible y-values for the function.
By examining the equation, we can see that the constant term +4 gives a y-intercept of 4. This implies that the graph will always be shifted upward by 4 units. Since the exponential term (-7(3/2)^x) is always negative, adding 4 to negative values will result in y-values greater than 4. Therefore, the range of the function is y > 4.
It's worth noting that the term "+4" does not create an asymptote. Asymptotes occur when the value of the exponential term approaches zero or becomes undefined. In this case, the graph approaches the x-axis but does not cross it due to the negative sign in front of the exponential term.