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elixir [45]
3 years ago
8

A cup of coffee has approximately 310 mg of caffeine. Each hour, the caffeine in your system decreases by about 35%. How much ca

ffeine would be left in your system after 5 hours? Round to the nearest whole.
Mathematics
1 answer:
Alex787 [66]3 years ago
3 0

Answer:

∴35.97 mg caffeine would be left in the system after 5 hours.

Step-by-step explanation:

Given that,

A cup of coffee has approximately 310 mg of caffeine.

Caffeine decrease at a rate 35% per hour.

Exponential Function:

y(t)=y_0(1-r)^t

y(t)= Amount caffeine after t hours

y_0= Initial amount of caffeine

r= rate of decrease

t = Time in hour.

Here y(t)=?, y_0 = 310 mg, r=35%=0.35, t= 5 hours

y(t)=310(1-0.35)^5

      =35.97 mg

∴35.97 mg caffeine would be left in the system after 5 hours.

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3 years ago
Given y = log3(x + 4), what is the range?​
lora16 [44]

Answer:

The range is all real numbers.

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Step-by-step explanation:

y=\log_3(x+4) only exists when x+4 is positive.

You can take the log of a negative or 0 number.

So x+4>0 implies x>-4.  (I just subtract 4 on both sides.)

So the domain is x>-4. You should see this also when you graph the curve that the curve only exist to the right of -4.

Now the range.  The range is where the curve exist for the y-values.

The equivalent exponent form of y=\log_3(x+4) is 3^{y}=x+4

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Also if you look at the graph of y=\log_3(x+4) you should see every y getting hit by the curve (look down to up; use the y-axis as a guide).

Let's think about the inverse I found above a little more (I'm going to swap x and y).

y=3^x-4.

If we look at the domain and range of this we can just swap it to get the domain and range of y=\log_3(x+4).

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Range : (-\infty,\infty)

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