Recursion
The swallowtail butterfly population grows at a rate of 7% monthly due to EPA efforts to reduce air pollution. If there were initially 3,000 butterflies in this environment, how many swallowtails will live in this area after 3 years (36 months)? -->
34,272 butterflies, WOW
Solve for x: log71 = x
x = 0
4 + 8 + 16 + ......... + 256
508
You've deposited $10,000 into a bank account with 1.8% interest rate compounded quarterly. What is the Effective Annual Interest Rate of this account?
***EAY = (1 + r/n)(n)(1) in the compound interest formula or (er1 ) in the compound continuously formula
1.01812 = 1.812% EAY
The number of fish in a nearby artificial lake decreases by 20% each year. To maintain the fish population,
the lake is restocked with fish at a rate of 30,000 fish per year. Suppose there are 280,000 fish in the lake
initially. Write a recursive system to model the number of fish in the lake, 𝐹(n), after n years.
F(n) = Fn-1(.8) + 30,000
Solve for HA: f(x) = log4(x - 9)
x = 9
3 + 1.5 + .75 + .375 + ...... + .00585
Approx. 5.994
Carbon-14 has been used to date the La Brea tar pits by testing remains of Saber tooth tigers. Carbon-14 has a half-life of 5,730 years. The initial mass of carbon-14 abundant in a saber tooth femur is 1 microgram.
a) Find a function that models the amount of the sample remaining t years after the Saber Tooth Tiger died.
*hint: use the formula of half life: A = p(1/2)(t/HL)
A = 1(1/2) ^ (t/5730)
The number of fish in a nearby artificial lake decreases by 20% each year. To maintain the fish population, the lake is restocked with fish at a rate of 30,000 fish per year. Suppose there are 280,000 fish in the lake initially. What will happen to the fish population in the long run?
150,000
Solve for x: log52 + log5x = 3
x = 62.5
Find the geometric sum if a=9/10, r=1/10, and k=99
.999; approx 1
Recently, you've received an unexpected $10,000 inheritance. You plan deposit this into a bank account with a 1.8% annual interest compounded daily. How much money will be in the bank account after 5 years?
(Hint hint, compound interest formula)
$10,941.72
The number of fish in a nearby artificial lake decreases by 20% each year. To maintain the fish population, the lake is restocked with fish at a rate of 30,000 fish per year. Suppose there are 280,000 fish in the lake initially. How many fish would need to be added to the lake each year for the population to stabilize at 225,000?
45,000 must be added per year!
Solve for x: log5252 = x
x = 4
5/2 + 5/22 + 5/23 + ..... + 5/210
4.99
You've deposited $1000 into a bank account with a 4% interest rate is compounded continuously. How much money do you have after 10 years?
$1491.82
Mrs. Belledin is having a pest problem in her garden. She wants to add 3,000 ladybugs per week to naturally solve the problem. The initial ladybug population in her garden is 50,000. The ladybug population decreases by 9% each week. How many ladybugs will she have after 4 weeks?
She will have 44,762 ladybugs! :D
Solve for x: log3(2x+6) = log3(42)
*Hint: one to one property
x = 18
6 - 18 + 54 - 162 + 486 -1458
1095
In your own words, describe what e represents.
max return on investment when you compound continuously