unit 7 review

classifying exponential functions

100

growth or decay?

y = 12(1.5)^x

growth

200

growth or decay?

y = 700(.75)^x

decay

300

growth or decay? what is the initial amount?

y = 2000(.25)^x

decay. initial amount: 2000

400

growth or decay? what is the % of growth/decay?

13(1.11)^x

growth by 11%

500

growth or decay? what is the % of growth/decay

46(.37)^x

decay. - 63%

construct a function

100

you are investing $3000 for at a rate of 9% a year.

construct a function based on this information.

3000(1.09)^x

200

a culture of bacteria has a growth rate and 3/5ths each hour. You collect a sample of 200 bacteria in a petri dish. construct a function that represents the growth of this sample.

200(1.06)^x

300

You are studying the effectiveness of a new cleaner at killing bacteria. It has been known to kill 84% of bacteria every minute it is left to soak. Create a function to represent this decay of 6000 bacteria. How many bacteria will remain of 6000 after the cleaner is left to soak for 3 minutes? round to the nearest hundredth.

6000(.16)^m

after 3 minutes: 24.58

400

you are looking to invest the money you made over the summer which totals to $2000. you can invest in bank A with a rate of 10% a year or in bank B with a rate of 2% a month. calculate how much money you could have after 1 year at each bank, rounding to the nearest cent. Which bank would be better to invest in?

bank A: 2000(1.1)¹ = $2200.00

bank B: 2000(1.02)¹² = $2536.48

bank B is better.

500

A sedative wears off at a rate of 3% each minute. 2500mg of this sedative is administered to a patient undergoing surgery. create a function to answer the following questions rounding to the hundredths place: 

How many mg of the drug will remain in the patient's system after 1 hour?

The sedative is considered inert when only 25mg remain. how long until this is the case?

2500(.97)^m

after 1 hour: 402.02 mg

inert after 151.19 min or approximately 2 hours and 31 min

converting between forms

100

convert to exponential form

log₅ 25 = 2

5² = 25

200

convert to exponential form

log₇ 2401 = 4

7⁴ = 2401

300

convert to logarithmic form

16³ = 4096

log₁₆ 4096 = 3

400

solve for x

log 100 = x

x = 2

500

solve for x

log₂₅ x = 1/2

x = 5

simplifying logs

100

solve for x

log₂ x = 2

x = 4

200

simplify

log₄ 64 =

log₄ 64 =3

300

simplify

log 1000 =

log 1000 = 3

400

simplify. round to the nearest hundredths place.

log₆ 300 =

log₆ 300 = 3.18

500

simplify

log₁₆ 4 =

log₁₆ 4 = 1/2

solving logs

100

solve for x

4^x = 4096

x = 6

200

solve for x. round to the hundredths place.

5(3^x) + 12 = 192

x = 3.26

300

solve for x. round to the hundredths place.

7^(4x-3)= 2401

x = 1.75

400

solve for x.

9^(x+2) = 3^(3x-12)

x = 16

500

solve for x. round to the hundredths place.

2ln(3x - 1) = 6

x = 7.03