Exponential and Logarithmic Functions

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Princezz3286

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Nov 12, 2005
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Here is an example problem from my book, I just don't understand how to get one of the numbers.

Suppose that an amount P0, in dollars, is invested in a savings account where interest is compounded continuously at 7% per year. That is, The balance P grows at a rate given by dP/dt = .07P.

a) find the function that satifies the equation. write it in terms of P0 and 0.07
P0e.07(t)

b) suppose that $100 is invested. What is the balance after 1 year.
P(1)= 100e.07(1)
=100e.07
=100(1.072508) <--- where does 1.072508 come from?
= $107.25

c)In what period of time will an investment of $100 double itself?

we can address c as soon as i figure out b.......

thanks in advance!
Heather
 
Hi. Google says that \(\displaystyle $e$\) raised to the power of 0.07 \(\displaystyle $\approx 1.07250818.$\)

I imagine your calculator will show a similar result. So, that's where that number comes from. You gotta love compounded interest.

Anyway, now that you know how the formula works, part (c) is probably a piece of cake. Just solve for t when the expression is equal to double the original amount, right?
 
ok, I see what you mean..... another question..... we are not allowed to use any calculator except for the one in our heads for the test..... is there a way to calculate e^.07 without my TI-89?
 
Princezz3286 said:
ok, I see what you mean..... another question..... we are not allowed to use any calculator except for the one in our heads for the test..... is there a way to calculate e^.07 without my TI-89?
Click to expand...

when x <1

e^x can be approximated as 1+ x + x^2/2
 
I suppose some people could compute it exactly, but I can't, and I don't know any of those people personally. You can estimate it, but prudence demands that I stay away from commenting on what you are and are not allowed to use on your tests, but I think it would be unfair to require you to take e to some decimal power without a calculator. No way you can do it. If you find yourself in that predicament on test day, look for another way to solve the problem (like, see if you can cancel the e out of an equation), because there must be at least one other way. Or, leave e in the answer.
 
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