The e^x Function: To e or not to e Examples

Calculate the population of Exponencity 15 years from now if there is a continuous growth rate of 4%. The population now is 36,295.

A = Per^t
A = 36295e^0.04(15)
A ≈ 66134

How many bacteria are there on the water fountain after 24 hours if a 10th grader, Buck Teeria, sneezed on it before taking a drink of water. 203 bacteria landed on the water fountain initially and then grew continuously at a growth rate of 21%.

First, build the exponential equation:

A = Per^t
A = 203e^0.21t

Now let's substitute 24 hours into the equation.

A = 203e^0.21(24)
A ≈ 31357

Quick! Someone grab the anti-bacterial spray.

If a cell phone lays around for 400,000 years. Use a carbon dating formula to find how much carbon is left if we started with 299 grams. The carbon decays at 0.00132%.

C = 299e^-0.0000132t
C = 299e^{-0.0000132*400000}
C ≈ 1.5

There is only 1.5 grams of cell phone carbon left. Pretty unrecognizable. More than likely, it's just a tiny little piece of "galaxy."