Answer:
y = 2x + 13
y = –x – 2
Step-by-step explanation:
The options are:
y = 2x + 13
y = -x - 2
y = 3x - 5
y= -(1/2)x + 6
y = -2x - 2
The graph is shown in the figure attached. There, point (-5, 3) is shown. Replacing it into the equations we get:
y = 2(-5) + 13 = 3 (so, it is a solution)
y = -(-5) - 2 = 3 (so, it is a solution)
y = 3(-5) - 5 = -20 ≠ 3 (so, it isn't a solution)
y= -(1/2)(-5) + 6 = 8.5 ≠ 3 (so, it isn't a solution)
y = -2(-5) - 2 = 8 ≠ 3 (so, it isn't a solution)
Given:
The exponential equations in the options.
To find:
The equation which represents exponential decay.
Solution:
The general exponential equation is
where, a is initial value and b is growth rate.
If b<1, then it is an equation of exponential decay.
If b>1, then it is an equation of exponential growth.
In option A, b=31>1, i.e., exponential growth.
In option B, b=3.1>1, i.e., exponential growth.
In option C, b=0.13<1, i.e., exponential decay.
In option D, b=1.03>1, i.e., exponential growth.
Only represents exponential decay.
Therefore, the correct option is C.