Aim: How do we solve real life situations leading to ...
Aim: How do we solve real life situations leading to exponential equations?
Do Now: If you won a contest and were given the choice of the following prizes, which one would you chose? Prize 1: $1000 if you collected the money on day 1, $2000 if you waited until day 2 to collect, $3000 if you waited until day 3 to collect and so on. You could collect your money at any time, or wait until the end of 20 days and collect it at that time.
Prize 2: $1 if you collected on day 1, $2 if you collected on day 2, $4 if you collected day 3, $8 if you collected day 4, and so on. You could collect money at any time or wait until the 20th day.
Jan 610:31 AM
Formulas to know
Compounded once in t time
• Growth (gain) A= P(1 +r)t
Keep in mind P is aka Ao
• Decay (loss) A= P(1 r)t
Compounded n times in t time r
nt • Growth (gain) A= P(1 + ) n
r nt • Decay (loss) A= P(1 ) n
Continuously A= Pert
P= Ao= Orginial amount (principle) r= rate (percentage) t= interval of time n= number of times compounded in one t
* Last 3 formulas are usually provided for you * Examples 1) If a bank compounds interest annually (once each year), then the amount of money, A, in a bank account is determined by the formula A = P(1+r)t. Here, P = the principal, or the amount invested, r = the rate of interest, and t = the number of years involved. If $100 is invested at 6% interest compounded annually, the amount, A, in the account is found by using the formula A = $100(1.06)t. A) Find the amount of money in this account at the end of 1 year. B) Find the amount of money in this account at the end of 5 years. C) Using a graphing calculator, find out how many years it would take for this account to grow to $200.
Jan 610:33 AM
2) Amanda won $10,000 and decided to use it as her "vacation fund". Each summer, she withdraws an amount of money that reduces her funds by 7.5% from the pervious year. How much money will be in her account after her 8th withdrawal?
3) If a bank compounds interest continuously at a rate of 5% and the initial deposit was $100, the amount in the account is represented by A = $100e0.05t where t represents the number of years. A) Find the amount of money in this account at the end of 1 year. B) Find the amount of money in this account at the end of 5 years.
4) The Franklins inherited $3,500, which they want to invest for their child’s future college expenses. If they invest it at 8.25% with interest compounded monthly, determine the value of the account, in dollars, after 5 years.
5) The decay constant of radium is 0.0004 per year. How many grams will remain of a 50 gram sample of radium after 20 years?
6) Find the interest that has accrued on an investment on an investment of $1,000 if interest of 4.5% per year is compounded quarterly for a year. Jan 610:33 AM
HW#54 #s 11, 12, 17a,b, 18a,b, 19, 23
Dec 2310:52 AM
Do Now: If you won a contest and were given the choice of the following prizes, which one would you chose? Prize 1: $1000 if you collected the money on day 1, $2000 if you waited until day 2 to collect, $3000 if you waited until day 3 to collect and so on. You could collect your money at any time, or wait until the end of 20 days and collect it at that time.
Prize 2: $1 if you collected on day 1, $2 if you collected on day 2, $4 if you collected day 3, $8 if you collected day 4, and so on. You could collect money at any time or wait until the 20th day.
Jan 610:31 AM
Formulas to know
Compounded once in t time
• Growth (gain) A= P(1 +r)t
Keep in mind P is aka Ao
• Decay (loss) A= P(1 r)t
Compounded n times in t time r
nt • Growth (gain) A= P(1 + ) n
r nt • Decay (loss) A= P(1 ) n
Continuously A= Pert
P= Ao= Orginial amount (principle) r= rate (percentage) t= interval of time n= number of times compounded in one t
* Last 3 formulas are usually provided for you * Examples 1) If a bank compounds interest annually (once each year), then the amount of money, A, in a bank account is determined by the formula A = P(1+r)t. Here, P = the principal, or the amount invested, r = the rate of interest, and t = the number of years involved. If $100 is invested at 6% interest compounded annually, the amount, A, in the account is found by using the formula A = $100(1.06)t. A) Find the amount of money in this account at the end of 1 year. B) Find the amount of money in this account at the end of 5 years. C) Using a graphing calculator, find out how many years it would take for this account to grow to $200.
Jan 610:33 AM
2) Amanda won $10,000 and decided to use it as her "vacation fund". Each summer, she withdraws an amount of money that reduces her funds by 7.5% from the pervious year. How much money will be in her account after her 8th withdrawal?
3) If a bank compounds interest continuously at a rate of 5% and the initial deposit was $100, the amount in the account is represented by A = $100e0.05t where t represents the number of years. A) Find the amount of money in this account at the end of 1 year. B) Find the amount of money in this account at the end of 5 years.
4) The Franklins inherited $3,500, which they want to invest for their child’s future college expenses. If they invest it at 8.25% with interest compounded monthly, determine the value of the account, in dollars, after 5 years.
5) The decay constant of radium is 0.0004 per year. How many grams will remain of a 50 gram sample of radium after 20 years?
6) Find the interest that has accrued on an investment on an investment of $1,000 if interest of 4.5% per year is compounded quarterly for a year. Jan 610:33 AM
HW#54 #s 11, 12, 17a,b, 18a,b, 19, 23
Dec 2310:52 AM
