Exam 2 TMath 120 Autumn 2018

NAME:

1. [6] TRUE/FALSBiJ^ircle T in each of the following cases if the statement is alwaystrue. Otherwise, circle F. Let x and y be positive real numbers.

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T (F^log(2; - y} =log{x) - log(y)

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^ c>ov '°c1^Show your work for the following problems. The correct answer with no

supporting work will receive NO credit.

2. [3] (WebHW7 #22) How long does it take for a deposit of $1400 to double at 3%compounded cc)Irt;umausl^'? ^~V ( ^

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4. [3] (§3.2 #56) The graph is of an exponential function log^(a;) that has been horizontallyshifted. Fiud the algebraic rule/write an equation for the graph.

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.^1:^^} -^%^) .^-s^5. For each equation below, find\fc. ^ ~~ '^—^ \J - --1.

(a) [3] (exponentActivity #3) (a- + I)-1 +3 =x

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(b) [3] (WebHW8 #21) Ql-x =

lU^-^SnC^'')1-x _ c5a;+6

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6. [3] (PracticeExam#6) The function f{x) = 3 • 2X + 5 passes the horizontal line test so ^yjg \y^ (.

has an inverse. Find f {x).

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7. [2] (Quiz3 #3) Write the following logarithmic statement in exponential form:

21og(,(a)=rc

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8. [3] Write a polynomial p that satisfied the following criteria:

• as x goes to oo, then y goes to —co ^. 7- "*"

• the only roots are: -1,2 and 4 ] ^t.'}-.

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9. [4] (WebHW6 #16) Find the remainder when x4 - 398x2 +1 is divided by x2 - 20x +1

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10. [3] (logProperties #3) Let logs^) = 7 and log2(y) = 6. Find log^(8xy)

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^^^^f^ —y^-^-^11. [4] CEITose ONE of the following. Clearly identify which of the two you are answering

and what work you want to be considered for credit.

No, doing both questions will not earn you extra credit.

(a) (WebHWQ #10) pH Scales: Let [H+] be the concentration of hydrogen ions insolution X measured in moles per liter (denoted M). Then

pH level of solution X = — \og[H+} ,

Suppose that hydrogen ion concentration in a solution A is 10,000 times that in

solution B. Find a function relating the pH level of solution A to the pH level ofsolution B. I °^ ^

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(b) (§3.2 #115) Benford's Law: r^e probability that the first decimal-digit of a rawdata sample (from 1 to 9) is/given by Pm = log(m + 1) — log(m).

What percentage of data would financial investigators expect the numbers inaccounting books to have 3 as a first digit?

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12. [5] Choose ONE of the following. Clearly identify which of the two you are answeringand what work you want to be considered for credit.

No, doing both questions will not earn you extra credit.

(a) (expActivity #5) Newton's Law of Cooling: If D is the initial temperature dif-

ference between an object and its surroundings, and ij-j.ts surroundings have a

temperature T, then the temperature of the object A-^d-time t is modeled by:

A = T + De~kt

where A; is a positive constant that depends on the type of object.

Initially coffee has a temperature of 200°F in a room that is 70°. After ten

minutes the temperature is 150 . What will the temperature of the coffee be afteran additional ten minutes passes?

(b) (§3.3 #108) Amortization formula: If r is the annual interest rate, M is the

mortgage amount, t is the number of years, and n is the number of payments a

year, then the payment P on a mortgage is given by:

r-M

1-(1+^) —nt —n

The Garcia family wanted to take out a mortgage for $150,000 with 8% with

monthly payments. The family can afford monthly payments of $1200. How

long would they have to make payments to pay off their mortgage and how much

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interest would they be paying?

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