Semester 2 review

exponential growth & decay

100

does this formula go with exponential growth or decay

y=a(1+r)^x

growth

200

exponential growth or decay

3(.5)^x

decay

300

exponential growth or decay

5(1.56)^x

growth

400

exponential growth or decay

14^-x

decay

500

the population of hometown in 2016 was estimated to be 35000 people with an annual rate of increase of 2.4%. what is the growth factor for hometown

1.024

properties of log

100

rewrite into logarithms

2⁴=16

log₂16=4

200

rewrite into logarithms

e⁴=54.60

ln54.60=4

300

write the expression as a single logarithmic quantity

log₂5 + log₂x - log₂3

log₂ 5x\3

400

write the expression as a single logarithmic quantity

1\2 log₅7 - 2log₅x

look on paper

500

condense the log

2(log 2x -log y) - (log 3 +2 log 5)

log 4x²\75y²

constant proportionality

100

determine if the relationship is proportional,if yes, determine the constant proportionality

days (x)           1      3     5      6

pages read (y)  100  300  550  600

if you take the ratios of x and y for all values, we don't get an equal vale. so its not proportional

200

find the value of y when x equals 7.

y=144   x=12

y=84

300

a taxi cost $40.50 for 15 miles, what's the cost for 20 miles

20 miles=$54

400

what is the value of x

(on white board)

x=5.4

500

one side of a box is 8.5in, given that the scale factor is 2in=5ft and the boxs are proportional, what is the side of the other box in ft

21.25ft

natural base & exponential function

100

what is the natural exponential function expressed as

e^x

200

what is the logarithmic function

y=log_ex or y=lnx

300

evaluate log₁₀ 1\e

-1

400

simplify ln (square root of xy)

1\2 (ln x + ln y)

500

simplify 5 ln (x+y) - 2ln y - 8 ln x

ln (x+y)⁵ \ y²x⁸