Midterm 2 Review w/ Probability

Exponential Functions

100

 A certain type of bacteria triples in number every hour. If we start with 20 bacteria, how many bacteria will there be after 5 hours?

4,860 bacteria

200

A drug’s concentration in the bloodstream decreases by 30% per hour. If a patient starts with 200 mg, how much is left after 5 hours?

33.6 mg

300

What interest rate is needed for $1 to become $2 in 1 year if compounded monthly?

 69.3%

400

A new car costs $30,000 and loses 12% of its value each year, compounded annually. How much will it be worth after 5 years?

$15,831

500

Emma deposits $1,000 in a bank that offers an annual interest rate of 5% compounded annually. How much money will she have after 4 years?

$1,215.50

Logarithmic Functions

100

Write the expression in logarithmic form.

7⁵ = 16807

log₇16807 = 5

200

Write the expression in logarithmic form.

16^3/4 = 8

log₁₆8 = 3/4

300

Write the expression in logarithmic form.

(1/3)^-2 = 9

log_1/39 = -2

400

Write the expression in exponential form.

log_1/51/625 = 4

(1/5)⁴ = 1/625

500

Write the expression in exponential form.

log₉1/81 = -2

9^-2 = 1/81

Evaluating Logarithmic

100

Determine the exact value without a calculator.

log₃81

4

200

Determine the exact value without using a calculator.

lne⁴

4

300

Combine each into a single logarithm with a coefficient of one.

2log₄X + 5log₄Y - 1/2log₄Z

log₄(x²y₅/z^1/2)

400

combine into a single logarithm with a coefficient of one.

3ln(t+5) - 4lnt - 2ln(s-1)

ln[(t+5)³/t⁴(s-1)²]

500

Combine into a single logarithm with a coefficient of one.

1/3loga - 6logb + 2

log (100 a^1/3/b⁶)

Exponential and Logarithmic Equations

100

log₄(x²-2x) = log₄

x=3, x=4

200

ln(x) + ln(x+3) = ln(20-5x)

x=2, x=-10 does not work

300

log₂(x+1) - log₂(2-x) = 3

x=5/3

400

log(x) = 2 - log(x-21)

x=25, x=-4 does not work

500

2log(x) - log(7x-1) = 0

x=0.1459, x=6.8541

Random

100

Start:185°F, room: 75°F, after 5 min: 160°F.

a)Find k

b) Find temperature after 15 min

a) k = -0.0517

b) T(15) = 125.66 Farenheit

200

5^1-x = 25

x = -1

300

Is this population growing exponentially, use semi-log plot to find out.

The data is collected over time shown below,

(0, 500) (1, 1000) (2, 2000) (3, 4000) (4, 8000)

Yes

400

Simplify [(z²y^-1x^-3)/(x^-8z⁶y⁴)]^-4

(z¹⁶y²⁰)/x²⁰

500

Simplify [((2x²)^-3)y⁴]/((6y)^-1)x^-7)

(3xy⁵)/4