Rates & Factors
Does the following equation model exponential growth or decay?
y=300(1.001)^t
Growth
Which is the best investment for $1000?
A) 5% interest compounded annually
B) 5% interest compounded continuously
C) 5% interest compounded monthly
B) 5% interest compounded continuously
What is the value of t (time) in the following problem?
"A man invested $2000 in a savings account when his first grandchild was born. The account held $4100 on the grandchild's eighteenth birthday. If the interest was compounded monthly, what was the annual interest rate?"
t=18
A savings account has $1,500 invested at an annual interest rate of 4%, compounded annually. How much money will be in the account after 6 years?
A=1500(1.04)^6
Solve (four decimal places):
ln(2x)-1=1.537
x=6.3208
If the growth factor is 1.57, what is the percentage of increase or decrease?
+57%
"You invest $12000 in an account with a 7.3% interest rate, compounded monthly. How long will it take for you to have $20000 in the account?"
What value would you put in place of ?:
20000=12000(1+(? )/12)^(12t)
.073
What is the INITIAL VALUE in the following word problem?
After driving it for three years, the car your parents bought you is now worth only $2130. If your parents paid $6500 for it, by how much did the value of the car depreciate each year?
P=6500
A car is currently worth $18,000, but the value depreciates by 11% each year. How long will it take for the car to reach a value below $10,000?
10000=18000(1-.11)^t
Solve (round to 2 decimals):
200000=180000(1.17)^t
t=0.67
If the decay factor is 0.9, what is the percentage of increase or decrease?
-10%
"You invest $12000 in an account with a 6.5% interest rate, compounded quarterly. How long will it take for you to have $20000 in the account?"
What value would you put in place of ?:
20000=1200(1+.065/?)^(?t)
4
What is the value of n in the following problem?
"After high school you plan to rent an apartment. The place you plan to live has a great starting price at only $500 a month, but the rent will increase by 20% each quarter. How much will your rent be at the end of two years?"
"Each quarter" means n=4
An investment grows to $9,400 after 10 years at an annual interest rate of 3.2%, compounded quarterly.
What was the original amount invested?
9400=P(1+.032/4)^(4*10)
Solve (four decimal places):
1600=1100(1+r)^5
r=.0778
**BONUS 100 POINTS: 7.78%**
What is the growth factor for a value that triples annually?
3
"You invest $12000 in an account with a 16% interest rate, compounded annually. How long will it take for your money to double?"
What value would you put in place of ?:
?=12000(1.16 )^(t)
24000
What is the value of r in the following problem?
The population of wild polar bears in a certain region of Alaska has been decreasing by 20% each year for the past decade. If there are now only 30 polar bears in the region, how many polar bears were there 10 years ago?
r=-0.20
A piece of equipment was purchased 4 years ago for $6,000 and is now worth $3,960. Find the annual rate of depreciation.
3960=6000(1-r)^4
Solve (four decimals):
0.758=0.983e^(k*100)
k=-.0026
What is the growth or decay factor for a value that decreases by 4.3% annually?
0.957
"You invest $12000 in an account with a 4% interest rate, compounded continuously. How long will it take for you to have $20000 in the account?"
Write the full equation you would use to solve this problem.
20000=12000e^(.04t)
What is the TIME (t) value in the following problem?
"In 1916, California established a state minimum wage of 16ยข per hour. If the minimum wage today is $16.50, what was the average annual percent increase?
t=109 years
A scientist is studying bacteria that multiplies continuously. The population of a culture increases from 220 cells to 500 cells in 9 hours. What is the growth constant of the bacteria?
500=220e^(9k
Solve (round to two decimals):
21400=P(1+.14/12)^(12*5)
P=10670.07