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The draining of the reservoir follows an exponential function
The reservoir will reach a depth of 10 feet at 7.6 hour
The given parameters are:
[tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex]
An exponential equation is represented as:
[tex]\mathbf{y = ab^x}[/tex]
Substitute [tex]\mathbf{(x,y) = (1,64)(4,28)}[/tex] in [tex]\mathbf{y = ab^x}[/tex]
[tex]\mathbf{64 = ab^1}[/tex]
[tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{28 = ab^4}[/tex]
Divide [tex]\mathbf{64 = ab}[/tex] and [tex]\mathbf{28 = ab^4}[/tex]
[tex]\mathbf{\frac{ab^4}{ab} = \frac{28}{64}}[/tex]
[tex]\mathbf{b^3 = 0.4375}[/tex]
Take cube roots
[tex]\mathbf{b= 0.76}[/tex]
Substitute [tex]\mathbf{b= 0.76}[/tex] in [tex]\mathbf{64 = ab}[/tex]
[tex]\mathbf{64 = 0.76a}[/tex]
Solve for a
[tex]\mathbf{a = 84}[/tex]
So, the equation is:
[tex]\mathbf{y = 84(0.76)^x}[/tex]
See attachment for the graphs of [tex]\mathbf{y = 84(0.76)^x}[/tex] and y = 10
The point of intersection is: x = 7.6
Hence, the reservoir will reach a depth of 10 feet at 7.6 hour
Read more about exponential functions at:
https://brainly.com/question/15352175
