Jason deposits $5 into his savings account twice a week for 6 weeks. How much money will he have saved after 6 weeks?

Mathematics

1 answer:

gregori [183]3 years ago

8 0

Answer:

$60

The equation is x(5(2))=s or x(10)=s when x = number of weeks

Step-by-step explanation:

For 6 weeks, all you have to do is plug in the 6 where the <em>x</em> is.

6(5(2)) = s

6(10) = s

60 = s

6(10) = s

60 = s

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A cup of coffee contains about 100 mg of caffeine. Caffeine is metabolized and leaves the body at a continuous rate of about 12%

Mamont248 [21]

Answer:

a. $A = C_{0}(1-x)^t\\x: percentage\ of \ caffeine\ metabolized\\$

b. $\frac{dA}{dt}= -11.25 \frac{mg}{h}$

Step-by-step explanation:

First, we need tot find a general expression for the amount of caffeine remaining in the body after certain time. As the problem states that every hour x percent of caffeine leaves the body, we must substract that percentage from the initial quantity of caffeine, by each hour passing. That expression would be:

$A= C_{0}(1-x)^t\\t: time \ in \ hours\\x: percentage \ of \ caffeine\ metabolized\\$

Then, to find the amount of caffeine metabolized per hour, we need to differentiate the previous equation. Following the differentiation rules we get:

$\frac{dA}{dt} =C_{0}(1-x)^t \ln (1-x)\\\frac{dA}{dt} =100*0.88\ln(0.88)\\\frac{dA}{dt} =-11.25 \frac{mg}{h}$