need to write an equation

Question

Claire has $300 in an account. She decides she is going to take out half of the money remaining in the account at the end of each month- I need to write an equation

Answer 1

This will be an exponential decay equation, because your bank balance is decreasing by half each month.  To see the desired pattern, you can write down the first few months' worth of remaining balances.

 

Month/Balance

0/300 (starting balance)

1/150 (1/2 of 300)

2/75 (1/2 of 75)

3/$37.50 (1/2 of $37.50)

 

There is a standard exponential equation form of y=ab^x ~ For this equation, a represents your initial conditions.  If you put x in for 0 the b part goes away (b⁰=1).  The b is your "decay factor" (or growth factor if the equation shows growth). In your case, the money is decaying at a rate of 1/2.

 

Your equation is B(t)=300(1/2)^t

 

I used B randomly to represent "balance"

I used t randomly to represent time, measured in months