SOLUTION: If all who hear a rumor repeat it to two people a day, and if 20 people start the rumor, then number of people N who have heard the rumor after t days is given by N(t) = 20(3)t.

Question 225276: If all who hear a rumor repeat it to two people a day, and if 20 people start the rumor, then number of people N who have heard the rumor after t days is given by N(t) = 20(3)t. After what amount of time will 1000 have heard the rumor?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

You're given n(t) =1000 and you've been asked to find t:

So solve for t we're going to "peel away" the rest of the right side (i.e. the 20 and the 3). We'll start by dividing both sides by 20:

Next, to get rid of the 3, we will need to use logarithms. If 50 and are equal then their logarithms are equal, too. (You should use a base for the logarithms that your calculator can handle. Usually base 10 or base e (aka natural) logarithms are best.):

Now we can use the property of logarithms, , to "move" the t out of the exponent:

We can now solve for t by dividing both sides by :

For our final answer we can use our calculator on the two logarithms on the left side:

Of course you can round off these decimals as you prefer.
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