Growth
In the exponential function given below, identify the initial amount and the growth rate:
y = 250(1 + 0.2)t
initial amount: 250
growth rate: 0.2
What is decay?
the change that occurs when an original amount is reduced by a consistent rate over a period of time
What is the compound interest formula?
What is A=P(1+r/n)nt
Evaluate log381
The population of Chicago starts at 20,000 and grows by 13% each year. Write an exponential growth model to find the population after 10 years.
y = 20,000(1.13)10
In the exponential function given below, identify the initial amount and the growth rate:
y = 9.8(1.35)t
growth rate: 0.35
initial amount: 9.8
A fully inflated child's raft for a pool is losing 6% of its air everyday. The raft originally contained 4,500 inches of air. Write an equation to represent the loss of air.
y = 4,500(1 - 0.06)t
William wants to have a total of $4000 in two years so that he can put a hot tub on his deck. He finds an account that pays 5% interest compounded monthly. How much should William deposit into this account initially so that he'll have enough to buy a hot tub?
$3,584.23
Rewrite 12x = 143 as a logarithm.
log12143
Account 1: Receives a deposit of $25 each month
Account 2: Earns 25% interest each month
Which account represents a linear quantity and which represents an exponential quantity?
Account 1: linear
Account 2: exponential
Write an exponential growth equation to show a population of 422,000 increases by 12% each year.
y = 422,000(1 + 0.12)t
A car bought for $13,000 decreases at 12% per year. What is its value after 7 years?
$5312.78
Sarah's parents invested in $14,000 at a rate of 6% per year, compounded monthly. How much money will there be in the account after 10 years?
$25,471.55
Rewrite log5115 = x as an exponential equation.
5x = 115
In 1985, there were 285 cell phone subscribers in a small town. The number of subscribers increased by 75% per year after 1985. How many cell phone subscribers were in the town in 1994?
43,871
The prize for a radio station contest begins with a $100 gift card. Once a day a name is announced. The person has 15 minutes to call or the prize increases by 3% for the next day. After 10 days with no winners, how much is the gift card worth?
$134
Each year the local country club sponsors a tennis tournament. Play starts with 128 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds?
4
When your friend was born, your friend's parents deposited $2000 in an account paying 4.5% interest compounded quarterly. What will the account balance be after 18 years?
$4,475.53
Evaluate 3t = 86
4.055
$1,500.00 is deposited in a bank paying an annual interest rate of 4.3%, compounded quarterly. What is the balance after 6 years?
$1,938.84
An initial population of 750 endangered turtles triples each year for 5 years. Find the population after 5 years.
182,250
If you buy a new truck for $28,700 where the value decreases continuously at 11% per year, how much will the truck be worth in 7 years? Round to the nearest dollar.
$12,694
Suppose that you will need $10,000 in thirty-six months' time when your child starts attending university. You want to invest in an account yielding 3.5% interest, compounded monthly. How much should you invest?
$9004.62
Your retirement contribution is in an account that earns 6% interest, compounded annually. If you deposit $10,000 initially, how many years will you have to work to have $2,000,000 saved?
90.93 years (lol)
In England in 1452 there were 10,000 people living in a city that was struck by a plague. After 6 days, there were only 8,500 people living. How many people were living after three weeks?
5,660