Solving Exponential Growth And Decay Problems

Solving Exponential Growth And Decay Problems-62
The general idea is that, instead of solving equations to find unknown numbers, we might solve equations to find unknown functions.

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The first problem that is show is exponential decay.

First you will need to create a table with hours and substance left.

This resource could be used as a prelude to the ' Power Demand' activity.

requires students to form equations given a set of cards and to determine, with examples, whether the equation is always, sometimes or never true and to attempt to say why.

Then, either repeating the method above or plugging into the formula derived by the method, we find $$c=\hbox = 1000$$ $$k==$$ $$== = (\ln 2)/4$$ Therefore, $$f(t)=1000\;e^=1000\cdot 2^$$ This is the desired formula for the number of llamas at arbitrary time $t$. At time $t=0$ it has $10$ bacteria in it, and at time $t=4$ it has $2000$. Solution: Even though it is not explicitly demanded, we need to find the general formula for the number $f(t)$ of bacteria at time $t$, set this expression equal to $100,000$, and solve for $t$.

Again, we can take a little shortcut here since we know that $c=f(0)$ and we are given that $f(0)=10$.

Since we've described all the solutions to this equation, what questions remain to ask about this kind of thing?

Well, the usual scenario is that some story problem will give you information in a way that requires you to take some trouble in order to determine the constants $c,k$.

The next step is to find the trend by noting that we are left with a certain percentage of the substance.

One you have the trend you will use this to calculate the amount of substance left in said hours, in this case 6 hours.


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