Answer: it is y=2.26x3.02^x
Step-by-step explanation:
Option D is correct.
An exponential regression is the process of finding the equation of the exponential function that fits best for a set of data.
[tex]y = ae^{bx}[/tex]
According to the question
We have a data.
Let the exponential regression equation be [tex]y = ae^{bx}[/tex]
Take two values of x and y from the given data for finding the value of a and [tex]e^{b}[/tex].
substitute y = 0.025 and x = -4 in [tex]y = ae^{bx}[/tex] we get
[tex]0.025 = ae^{-4b}...(1)[/tex]
similarly ,substitute y = 0.075 and x = -3 in [tex]y = ae^{bx}[/tex] we get
[tex]0.075 = ae^{-3b} ....(2)[/tex]
from equation 1 and 2
[tex]\frac{0.025}{0.075} = \frac{ae^{-4b} }{ae^{-3b} }[/tex]
⇒[tex]\0.333 = e^{-b}[/tex]
⇒[tex]ln(o.33) = -b[/tex]
⇒[tex]-(1,1086) = -b[/tex]
⇒ b = 1.1086
Therefore,
[tex]e^{b} = (2.718)^{1.1086} = 3.0041[/tex]
and substitute b = 1.1086 and [tex]e^{b} = 3.0041[/tex] in either equation 1 or 2, we get
a = 2.2
Thus, the exponential regression equation will be
[tex]y = (2.2)3.041^{x}[/tex]
Hence, option D is the correct one.
Learn more about exponential regression equation here:
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