Exercise 13 Page 479

y=t* (2* 10^6) Here y represents the number of red blood cells produced in t seconds. We want to determine how long it will take to replace the red blood cells lost by donating one pint of blood. There are 2.4* 10^(12) red blood cells in one pint of blood. Therefore, we want to know what t will be when y= 2.4* 10^(12). It will take your body about 1.2* 10^6 seconds to replace the red blood cells. We are also asked to give our answer in days. Let's convert 1.2* 10^6 seconds to days! From Part A we know the following. 1day =24* 60* 60s First, we will write this result in scientific notation.

24* 60* 60

▼

Write in Scientific Notation

\WriteProd

24* 6* 10* 6* 10

CommutativePropMult

Commutative Property of Multiplication

24* 6* 6* 10* 10

Multiply

Multiply

864* 10* 10

ProdToPowTwoFac

a* a=a^2

864* 10^2

Rewrite

Rewrite 864 as 8.64* 10^2

(8.64* 10^2)* 10^2

AssociativePropMult

Associative Property of Multiplication

8.64*(10^2* 10^2)

MultPow

a^m*a^n=a^(m+n)

8.64* 10^4

Next we can form the conversion factor. 1day =8.64* 10^4sec ⇒ 1day/8.64* 10^4sec Finally, using this conversion factor we will convert 1.2* 10^6sec to days.

1.2* 10^6sec*1day/8.64* 10^4sec

▼

Simplify

MoveLeftFacToNum

a*b/c= a* b/c

1.2* 10^6sec* 1day/8.64* 10^4sec

CancelCommonFac

Cancel out common factors

1.2* 10^6 sec* 1day/8.64* 10^4 sec

SimpQuot

Simplify quotient

1.2* 10^6* 1day/8.64* 10^4

MultByOne

a * 1=a

1.2* 10^6days/8.64* 10^4

WriteProdFrac

Write as a product of fractions

1.2/8.64*10^6/10^4days

UseCalc

Use a calculator

≈ 0.14*10^6/10^4days

DivPow

a^m/a^n= a^(m-n)

≈ 0.14* 10^2days

CalcPow

Calculate power

≈ 0.14* 100days

Multiply

Multiply

≈ 14days

It will take your body about 14 days to replace the red blood cells lost by donating one pint of blood.