If you invested $500 into a bank account earning continuously compounded interest and the value after 6 years is $614.99, find the interest rate. write your answer as a percent rounded to the nearest hundredth.

r = 3.45%

Step-by-step explanation:

You need the formula for continuously compounding interest, which is

A = Pe^(rt) , where

A is the total amount of money in the account,

P is the initial investment

e is a constant that represents continuous growth

r is the interst rate as a decimal (which we will be solving for)

t is how many years the interest was compounded

Plug in the given information

 614.99 = 500e^(r6)           (we need to solve for r)

614.99/500 = e^(6r)           (divide both sides by 500, simplify the righ side)

      1.22998 = e^(6r)       (simpligy the left side)

When using 'e', we can take the natural log of both sides of the equation and use rules for logarithms to simplify further...

 ln (1.22998)  =  ln (e^(6r)

     ln (1.222998) = (6r)(ln e)      (exponent rule for natural logs lets us bring

                                                     down any exponents as multipliers  

     ln (1.22998) = 6r                 (ln e = 1, you can verify this on your calculator)

   ln (1.22998)/6 = r        (divide both sides by 6 to isolate r)

     .034499652 = r          (Use a calculator to simplify the left side)

We need to write r as a percent, rounded to the nearest hundredth, so multiply r by 100%, then round

  (0.034499652)(100%) =   3.4499652%  

Rounding gives 3.45%

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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