<p>Ok so I'm taking AP Calc BC next year, and I'm doing a summer packet, but I don't know if my answers are right. Any help would be appreciated!!!!!</p>
<p>1.) The population of Standardsville is 500,000 and is increasing at the rate of 3.75% each year. Approximately when will the population reach 1 million?</p>
<p>I got 18.83 years</p>
<p>2.) THe half-life of a phosphorus-32 is about 14 days. There are 6.6 grams present initially.
a) Express the amount of phosphorus-32 reamining as a function of time t.</p>
<p>y=6.6e^(ln(.5)/14)t</p>
<p>b) When will there be 1 gram remaining?</p>
<p>1=6.6e^(ln(.5)/14)t</p>
<p>.1592 = t, but what units?</p>
<p>3.) Determine how much time is required for an investment to triple of interest is earned at the rate of 4.25% rounded weekley (52 wks/yr.)</p>
<p>NO IDEA! </p>
<p>4.) Suppose that a colony of bacteria starts with 1 bacterium and doubles in number every half house. How much bacteria will the colony contain at the end of 24 hours?</p>
<p>I got 2.815 x 10^14</p>
<p>1) P=Pe^(rt), solving for t. I got 18.48, maybe a difference in rounding</p>
<p>2) Wrong Formula!
a) P=P(1/2)^(t/h), t= time, h=half-life
b) Your units will be in days b/c that is the only time unit presented. </p>
<p>3) P=P(1+r/n)^(nt), r=rate (.1425), n=number of times (52 wks/year), P/P = 3</p>
<p>4) P=P(1+r/n)^(nt) or a term in a geometric sequence (a<em>1=1, r=2, n=49, solve for a</em>n)
I also got 2.815 * 10^14</p>
<p>Pretty sure this isn’t calculus. Someone can correct me if I’m wrong, but those look like algebra problems to me.</p>
<p>It isn’t calc, but it is summer work for Calc, so they’re probably making him review his stuff from Pre-Calc.</p>
<p>It’s not calculus, but exponential stuff and logs (which are the topics in the above problems) are part of the Calculus curriculum.</p>
<p>hey jalmoreno i think for the first problem you have it compounded continuously rather than annually… correct me if i’m wrong :P</p>
<p>Yeah I compounded it continuously, but that is usually how you treat population growth. Nor does the problem tell you about being compounded a specific number of times, unlike the bacteria problem.</p>