DOC PREVIEW
U of U MATH 1030 - Midterm 2 - Finances, Exponentials, and Modeling

This preview shows page 1-2-3 out of 8 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 8 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Midterm 2 - Finances, Exponentials, andModelingMath 1030 - Dylan Zwick’s C lassFall 2007Name:Financial Math FormulasCompound Interest Formula for Annually Compounding InterestA = P × (1 + AP R)YCompound Interest Formula for Interest Paid n Times Per YearA = P ×1 +AP Rn(nY )Compound Interest Formula for Continuous CompoundingA = P × eAP R×YA = accumulated balance after Y yearsP = starting principalAPR = annual percentage rateY = number of years1Savings Plan Formula (Regular Payments)Note - Assumes same times for payments and compounding periods,which will be the case on all problems in this midterm.A = P MT ×1 +AP Rn(nY )− 1AP RnPMT = regular payment (deposit) amountn = number of payment p eriods per yearOther Variables as B eforeExponential FormulasFormula for Exponential Growth with the Doubling Timey(t) = y0× 2t/TdoubleFormula for Exponential Decay with the Doubling Timey(t) = y0×12t/T12y(t) = amount after time ty0= initial amount (amount at t=0)Tdouble= doubling timeT12= half-lifeTdouble=log 21 + rr = growth rate (expressed as a decimal)Logarithm Ruleslog10(ab) = log10(a) + log10(b)log10ab= log10(a) − log10(b)log10(ab) = b log10(a)loga(b) =log10(a)log10(b)21. Compound and Simple Interest (10 points)Suppose you invest $1000 in an account today, planning to use it fora year long world trip when you retire in 40 years. If you invest at a5% APR interest, compounding a nnua lly, how much money will youhave for your trip when you retire? (5 points)How much money would you have if, instead of compounding a n -nually, your interest compounded continuously? (4 points)What is the APY for continuous compounding when the APR is 5%.(1 point)32. Savings Plans (10 points)Suppose you’re smart and start saving for retirement when you’re 20years old. You in vest $1, 000 each month for 45 years. If your APR is4.5%, compounded monthly, how much money will you have whenyou retire? (4 points)Suppose on the other hand that you would like to retire with $2, 000, 000.Given the same set up as above (45 years, 4.5% APR, compoundingmonthly) what would your monthly payments nee d to be? (3 points)Suppose that instead of making payments every month you put downone lump sum at the start. What would this lump sum need to be foryou to have $2, 000, 000 when you retire, using the same setup as thefirst two parts of this problem. (3 points)43. Exponential Growth (10 points)State whether each is a case of linear or exponential growth: (3 points)(a) A town whose population increases by 450 people every year.(b) A town whose population increases by 3% every year.(c) Compound interest.If a town’s population is 10, 000 in 2007 and doubles every 5 years,what will its population be in 2022? (2 points)Suppose one bacteria starts out in a bottle at 9:00 AM and the numberof bacteria in the bottle double every minute through mitosis. If thebottle is full at 10:00 AM, at what time will the bottle be half full? (2points)If you have an account that generates 5% APR interest and is com-pounded annually, how long does it take for invested money to dou-ble as a result of interest? In other words, if you put $1000 in the ac-count and left it there, how long would it take for you to earn enoughinterest so that you’ve got $2000 in the account? (3 points)54. Functions and Logarithms (10 p oints)Can a function have more than one input with the same output?(Yes/No) (1 point)Can a function have more than one output with the same input?(Yes/No) (1 point)The domain of a function is all possible inputs? (True/False) (1 point)The range of a function is all possible outputs? (True/False) (1 point)For the function f (x) = x2is the function one-to-one? (Yes/No) (1point)What are the domain and range of the function f (x) = x2? (2 points)If an odd function is periodic with pe riod 3 and if f(1) = 2 what isf(−4)? (3 points)65. Linear and Exponential Models (10 points)Suppose you start trick-or-treating with 10 candies, and each houryou get another 30 candies. How many candie s do you have after 3hours? (2 points)What is the equation for the line that passes through the points (3, 5)and (5, 9)? (5 points)If there are 100 mG of an antibiotic in the bloodstre am, and the drugdecreases exponentially with a half-life of 12 hours, how much an-tibiotic will be in the bloodstream after 15 hours? (3 points)76. Extra Credit (10 points)LogarithmsSolve for x in the following equations:(a) 47 = 3x(2 points)(b) x = log3(7) (2 points)(c) 99 = 12 × 4x(2 points)For each of the following organizations or individuals indicate whetherthey a re self declared Sunni or Shia Islam:(3 points for 6/6, 2 points for 5/6, 1 point for 4/6)(a) Hezbollah -(b) Nouri al-Maliki -(c) Hamas -(d) Mahmoud Ahmadinejad -(e) Bashar al-Assad -(f) Pervez Musharraf -Who is the President of Iraq? (1


View Full Document

U of U MATH 1030 - Midterm 2 - Finances, Exponentials, and Modeling

Download Midterm 2 - Finances, Exponentials, and Modeling
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Midterm 2 - Finances, Exponentials, and Modeling and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Midterm 2 - Finances, Exponentials, and Modeling 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?