SAVINGS ACCOUNT Demetrius deposits $120 into his account. One week later, he withdraws $36. Write an addition expression to repr
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To get started, we will use the general formula for bacteria growth/decay problems:
where:
A_{f} = Final amount
A_{i} = Initial amount
k = growth rate constant
t = time
For doubling problems, the general formula can be shortened to:
Now, we can use the shortened formula to calculate the growth rate constant of both bacteria:
Colby (1):
per hour
Jaquan (2):
per hour
Using Colby's rate constant, we can use the general formula to calculate for Colby's final amount after 1 day (24 hours).
Note: All units must be constant, so convert day to hours.
Remember that the final amount for both bacteria must be the same after 24 hours. Again, using the general formula, we can calculate the initial amount of bacteria that Jaquan needs:
where:
A_{f} = Final amount
A_{i} = Initial amount
k = growth rate constant
t = time
For doubling problems, the general formula can be shortened to:
Now, we can use the shortened formula to calculate the growth rate constant of both bacteria:
Colby (1):
Jaquan (2):
Using Colby's rate constant, we can use the general formula to calculate for Colby's final amount after 1 day (24 hours).
Note: All units must be constant, so convert day to hours.
Remember that the final amount for both bacteria must be the same after 24 hours. Again, using the general formula, we can calculate the initial amount of bacteria that Jaquan needs:
Set up the ratios as proportional fractions:
We can simplify the first fraction to make the problem easier. Both the numerator and denominator of the first fraction can be divided by 3:
Both fractions now have the same denominator. Since both fractions have to equal each other, the numerators will also be the same. Therefore, x = 4.
We can simplify the first fraction to make the problem easier. Both the numerator and denominator of the first fraction can be divided by 3:
Both fractions now have the same denominator. Since both fractions have to equal each other, the numerators will also be the same. Therefore, x = 4.