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In order to keep a specific bacteria alive, the tempature in a science lab, cannot exceed -20F. The electricity went out, when the tempature was -72F, but is increasing at a rate of 6.5 per hour. How many hours do the scientist have until the bacteria is not safe?

Respuesta :

MrRoyal

Answer:

At most 8 hours

Step-by-step explanation:

Given

[tex]Maximum = -20F[/tex]

[tex]Rate = 6.5/hour[/tex]

[tex]Base\ Temperature =-72F[/tex]

Required

Determine the time taken

Represent time by t.

The relationship between all parameters is:

[tex]Maximum = Base\ Temperature + Rate * t[/tex]

[tex]Base\ Temperature + Rate * t \leq Maximum[/tex]

This is so (≤) because, according to the question, the temperature can not exceed the maximum.

So, we have:

[tex]-72 + 6.5*t \leq -20[/tex]

[tex]-72 + 6.5t \leq -20[/tex]

Collect Like Terms

[tex]6.5t \leq -20 + 72[/tex]

[tex]6.5t \leq 52[/tex]

Solve for t

[tex]t \leq 52/6.5[/tex]

[tex]t \leq 8[/tex]

Hence, they have at most 8 hours

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