Question

Engineers are draining a water reservoir until its depth is only 10 feet. The depth decreases exponentially as

Answer 1

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:

$\mathbf{(x,y) = (1,64)(4,28)}$

An exponential equation is represented as:

$\mathbf{y = ab^x}$

Substitute $\mathbf{(x,y) = (1,64)(4,28)}$ in $\mathbf{y = ab^x}$

$\mathbf{64 = ab^1}$

$\mathbf{64 = ab}$

$\mathbf{28 = ab^4}$

Divide $\mathbf{64 = ab}$ and $\mathbf{28 = ab^4}$

$\mathbf{\frac{ab^4}{ab} = \frac{28}{64}}$

$\mathbf{b^3 = 0.4375}$

Take cube roots

$\mathbf{b= 0.76}$

Substitute $\mathbf{b= 0.76}$ in $\mathbf{64 = ab}$

$\mathbf{64 = 0.76a}$

Solve for a

$\mathbf{a = 84}$

So, the equation is:

$\mathbf{y = 84(0.76)^x}$

See attachment for the graphs of $\mathbf{y = 84(0.76)^x}$ 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:

brainly.com/question/15352175