The exponential function that contains the points (0,−5) and (4,−80) is:
y = -5(2ˣ)
An exponential function is given by:
y = a(bˣ)
where y, x are variables, a is the value of y when x is 0, and b is a constant.
Given the points (0,−5) and (4,−80):
We can deduce that a = -5, since when x = 0, y = -5. The equation becomes:
y = -5(bˣ)
At point (4,−80):
-80 = -5(b⁴)
16 = b⁴
[tex]b=\sqrt[4]{16} \\\\b=2[/tex]
Hence the exponential function is: y = -5(2ˣ)
