Exponential and Logarithms

Exponents

100

y = -2^(-x+3) +2

What transformations took place?

1) Reflect over X and Y

2) Right 3

3) Up 2

200

27^2x-1 = 2187^3x

Solve

x = -1/5

300

4^(x^2+7x) * 4^6 = 16^x

Solve

X = -3,-2

400

Log₃x^2-16x+69 = 2

Convert to exponential form and solve

X = 10, 6

500

3^(x^2 + 10x) * 3^(-4x+5) = 9^x

Solve

x= -2+i, -2-i

Logarithms

100

y = log(-(x-2))+1

List the transformations

1) reflect over y

2) right 2

3) up 1

200

log (base e) X = ln X

True or False

(10 sec)

True 

300

Log (base 2) (X^2+2) - 2 Log (base 2) X + Log (base 2) y^2 - Log (base 2) Z^2

Condense

Log (base 2) ((y^2*x^2 + 2y^2)/(z^2*x^2))

400

ln ((x^3*y^2*Z)/W*T^2)

Expand

3ln x +2 ln y + ln Z - ln W - 2ln T

500

ln 2x^2+8x+12 = ln x^2 + x

solve (RAPID ROUND)

20 Sec

x = -4,-3

Change of Base

100

Log (base 2) 8 = Log (base 8) 2

True or False

False

200

log (base 3) 10

Use log of base to solve and round to nearest thousandth (15 sec)

2.096

300

log (base 20) 100

Use change of base and round to nearest thousandth (15sec)

1.537

400

log (base 4) 9.2 = 2x +1

solve (round to nearest thousanth)

x = 0.301

500

What is log (base 2) C * log (base C) 2

Rapid Round 10 sec

1

Half Life/Interest

100

100 g Ion decays at 4% rate what is the Half Life?

Formula = y = a(1-r)^t

Round to nearest hundredth (45 sec)

16.98 years

200

A game costs $4000 and you have $2000 to invest and it has a 3.15% annual interest compounded monthly, how long would it take?

Round to hundredth.

22.03 years

300

Suppose you didn't know the starting value and the value of t was 10 what is p? (This is a add on of 200)

Round to nearest whole number

$2920

400

After 24 days 2mg of 128 mg sample remains what is the Half Life?

4 days

500

A radioactive isotope decayed to 17/32 of the original mass after 60 months, what is the Half Life?

round to nearest hundredth.

65.75 min

Newton's Cooling/PH word Problems

100

pH = -log[H+]

A solution with 5.5 * 10^-2 M of HBr what is the pH?

Round to hundredth

1.26

200

A solution is 2.5 * 10^-4 M HCl what is the pH and pOH?

pH = -log[H+]

pH + pOH = 14

pH =3.6

pOH = 10.4

300

A cake has a temp of 400F, the room temp is 75F after 12 minutes the cake is 325F, what is the rate?

T(t) = (T - A)e^kt +A

Round to nearest thousandth

-0.022

400

Add on of previous question.

What is t when the temp is 150F

Round to hundredth

Rapid Round (25 sec)

66.96 mins

500

Make your own question and solve. 

75 seconds

It can vary