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The level of water in a draining pool can be modeled with the function d(t)=12(.72)^t, where d is the depth of water, measured in feet, and t is the amount of time it's been draining, measured in days. Inayah claims that the pool is draining at a rate of 1.36%per hour. Is she correct? Explain

Answer :

Answer:

She is not correct, the claim is wrong

Step-by-step explanation:

Here, we want to check if a claim

made is correct

We can represent the exponential function as;

y = I( 1 - r)^t

So in this case;

1 - r = 0.72

r = 1 - 0.72

r = 0.28

This is same as 28%

So what this mean is that we expect a decrease of 28% per day

There are 24 hours on a day

So the decrease per hour will be 28%/24 = 1.167%

So as we can see the claim is wrong

MrRoyal

The model of the level of water in a draining pool is an illustration of an exponential function.

Inayah's claim is incorrect, because the water drains at 28% per hour

The function is given as:

[tex]\mathbf{y = 12(.72)^t}[/tex]

An exponential function is represented as:

[tex]\mathbf{y = a(1 - r)^t}[/tex]

Where r represents the rate.

So, by comparison

[tex]\mathbf{1 - r = 0.72}[/tex]

Collect like terms

[tex]\mathbf{- r = 0.72 - 1}[/tex]

[tex]\mathbf{- r = -0.28}[/tex]

Multiply both sides by -1

[tex]\mathbf{r = 0.28}[/tex]

Express as percentage

[tex]\mathbf{r = 28\%}[/tex]

This means that, the water drains at 28% per hour

Hence, Inayah's claim is incorrect

Read more about exponential functions at:

https://brainly.com/question/15352175

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