Tuesday

September 30, 2014

September 30, 2014

Posted by **John** on Sunday, September 5, 2010 at 1:29am.

P(t)= P(i)e^kt, where P is population, t is time, k is a constant and P(i) is the initial p or "p naught"; sorry, I don't know the typed notation for subscript. By the way, p(i) is given as 100.

The problems are

a.) "Find the expression after t hours"

b.) "Find the number of bacteria after t hours."

The answer to a is(via back of the book) is: 100(4.2)^t

I'm not sure exactly how to get there though I believe it has to do with taking natural logarithms and solving for e^k but since p is a function of t I'm not sure how to differentiate "k" (treat it as a constant or differentiate implicitly). If you could show the step by step process I'd appreciate it.

I got to: p(t)= 100(e^t+e^k) and stalled out.

Thanks in advance!

- Math (Calculus II) -
**drwls**, Sunday, September 5, 2010 at 2:06amWithout some specific numerical information on growth rate or the value of k, I don't see how that back-of-the-book equation can be derived. Is t in seconds in the original equation?

I also don't see the difference between "the population" and "the number of bacteria"

**Answer this Question**

**Related Questions**

Math - The size of a bacteria population is given by P=C*e^(kt) Where C is the ...

Math (Calculus II) - Rate of change proportional to size: P(t)= P(i)e^kt, where ...

maths --plse help me.. - A bacteria culture has an initial population of 600. ...

Algebra - Solve. The population of a particular city is increasing at a rate ...

Calculus AB - The rate of growth dP/dt of a population of bacteria is ...

Calculus - Suppose that you follow the size of a population over time. When you ...

precal - You can find the size of a population after t years using the formula N...

calculus - The population of a certain community is increasing at a rate ...

Calculus - The growth rate of Escherichia coli, a common bacterium found in the ...

precal - You can find the size of a population after t years using the formula N...