serious issues with some problems.
1. The ABC corporation issues a bond that pays 10,000$ after 10 years. If the initial investment is 5,000$ what is the interest rate per year, compounded annually.
The equation to use is A = P ( 1 + r )^t
Where A = Ending amount
P = Starting amount
r = interest rate
t = time
Right now I have this
10,000 = 5,000 ( 1 + r ) ^ 10
2 = ( 1 + r ) ^ 10
But i'm not sure where to go from here. Any ideas?
2. Mary wants to invest money in a 7-year saving certificate with an interest rate of 6% per year, compounded continuously. How much will she need to invest to have $1000 at the end of the term.
This uses the equation A = Pe^rt Where all variables have the same value is before, and of course e is e (2.7.........)
So far I have
1000=Pe^(7 x .06)
1000=Pe^.42
And now I have no idea what to do
3. Write the estimate in exponential form (Using the definition of a logarithm)
With this one I have absolutely no idea what I should do.
4. A water filter is constructed from a foam that REMOVES 25% of impurities for each inch of foam. How many inches of foam are needed for the filter to remove 50% of the impurities.
I know that this can be modeled with
and also with A = Pe^(rx)
P = concentration of impurities before filtration
A = concentration of impurities in filtered water
x = thickness of foam
I understand that
But I can't move much further from there.
Please don't just give answers. I really need to understand how to solve each problem. Thank you in advance.