Word problem #2

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caligirl350

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Feb 8, 2010
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The amount of particulate matter left in solution during a filtering process is given by the equation P = 600(2)-0.4n, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5.

Sorry everyone, this is the last one. Does the 600(2) get multiplied? Kinda lost on this one?
 
In your previous posts, you have not always typed expressions properly, so I'm going to guess that the product -0.4n is an exponent.

\(\displaystyle P = 600(2)^{-0.4n}\)

If this is the actual formula for P, we do not multiply 600 by 2.

We need to follow the Order of Operations; therefore, the exponentiation needs to be done before multiplying the power of 2 by 600.

Also, when typing exponents with a keyboard, we use the caret symbol ^ (as shown below).

EG:

Find the value of P when n is 10.

1) Substitute 10 for n

P = 600(2)^(-0.4*10)

2) Multiply -0.4 by 10

P = 600(2)^(-4)

3) Raise 2 to the power of -4

P = 600(1/16)

4) Multiply the power of 2 by 600

P = 600/16

5) Reduce the fraction to lowest terms

P = 75/2

Alternatively, you could put the entire expression for P (with parentheses around the exponent) into a scientific calculator.

600 * 2 ^ (-0.4 * 10 )

Press enter, and the calculator will display 37.5
 
caligirl350 said:
I am not sure if I am plugging this in correctly

600^2(-0.45)=600,150
Click to expand...

When you write "plugging this in", I'm not sure whether you're referring to plugging the expression into a calculator versus substituting the given values of n working with paper and pencil.

Let's go with the latter (working with paper and pencil).

The equation that you wrote above is wrong, for two reasons.

You raised 600 to an exponent, but 600 is not the base. The base on the exponent is 2. So, you need to raise 2 to the exponent first, and then multiply the result by 600 last.

Also, remember that the exponent is -0.4*n (in other words, the number -0.4 TIMES the number n). You wrote the substitution of n = 5 as -0.45. It should be -0.4*5, instead.

Here is how we write the given equation, substituting the number 5 for n:

P = 600*2^(-0.4*5)

The Order of Operations tells us to multiply -0.4 times 5 first.

P = 600*2^(-2)

The Order of Operations tells us to next raise 2 to the exponent -2.

P = 600*(1/4)

Now we multiply the power of 2 by 600.

P = 600/4

And this ratio obviously reduces.

P = 150

Can you now try the other one, where you substitute zero for n, instead?
 
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