simple exponential function problem

[flyingfreedom]

I don't really understand why they have the "e" in the equation. Shouldn't the equation look like this: 5000*1.03^10

[attachment=0:13li6kzm]ScreenHunter_05 Jan. 18 15.31.gif[/attachment:13li6kzm]

From the answer key the answer is B. How would this usually be solved?

 

[royhaas]

Use \(\displaystyle 5000 e^{.03 \times 10}\).

 

[Denis]

I don't really understand why they have the "e" in the equation. Shouldn't the equation look like this: 5000*1.03^10

Go here for "e" explanation: http://cs.selu.edu/~rbyrd/math/continuous/

 

[mmm4444bot]

… Shouldn't the equation look like this: 5000*1.03^10 …

Yes -- it should not.

The expression 5000(1 + 0.03)^10 gives the future balance if $5,000 is invested at 3% interest compounded annually for ten years.

5000 * e^(0.03 * 10) is for continuous compounding. Continuous compounding is exponential growth.

Exponential growth is not the same as "annual compounding".

Expressions for exponential growth or decay (eg: money, populations, radioactive mass) always contain the constant e.

 

[flyingfreedom]

Thanks a lot, you guys are the greatest!