1 / 11

Suppose Marcello invests $500 at 1.2% annually. How long will it take for that amount to double?

Suppose Marcello invests $500 at 1.2% annually. How long will it take for that amount to double?. Better than investing annually?. e (2.71828…): the natural base It represents the base rate of growth shared by all continuously growing processes.

audra-knowles
Download Presentation

Suppose Marcello invests $500 at 1.2% annually. How long will it take for that amount to double?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Suppose Marcello invests $500 at 1.2% annually. How long will it take for that amount to double?

  2. Better than investing annually?

  3. e (2.71828…):the natural baseIt represents the base rate of growth shared by all continuously growing processes.

  4. e (2.71828…):the natural baseQ: Why the natural base?A: Because it shows up in population growth, radioactive decay, and in systems that exhibit continuous growth or decay.

  5. Suppose we applied a (theoretical) continuous growth rate to an investment. Continuously Compounding Interest Formula:A = Pert

  6. A = PertNote that the expression has been substituted with er now.

  7. Take Tacoma’s population (as of 2012) of 202,010 which was growing at 1.8%. If the growth rate remains the same, what will its population be in 2013? Continuously Compounding Interest Formula:A = Pert= 202,010e0.018*3= ~213218

  8. If Portland, with its 2012 population of 603,106, is continuously growing at 1.7% then what will its population be in 2017? It’s e-asy!

  9. How e-nteresting Portland, with its 2012 population of 603,106, is continuously growing at 1.7%. When what will its population surpass 700,000?700,000 = 603,106e0.017t[solving for t!]1.16065… = e0.017t[divide by 603,106]loge1.16065 = 0.017t[put into log form,and with a base of e]0.148987… = 0.017t[evaluate dat log]8.76 396… = t[divide by 0.017]

  10. Portland, with its 2012 population of 603,106, is continuously growing at 1.7%. When what will its population surpass 800,000? e-nsane in the Membrane

  11. oh btw logex = ln(x)The natural basedeserves a natural logarithm.So from now on, instead of using loge(3),a shortcut to use is now ln(3).

More Related