classifying exponential functions
growth or decay?
y = 12(1.5)x
growth
you are investing $3000 for at a rate of 9% a year.
construct a function based on this information.
3000(1.09)x
convert to exponential form
log5 25 = 2
52 = 25
solve for x
log2 x = 2
x = 4
solve for x
4x = 4096
x = 6
growth or decay?
y = 700(.75)x
decay
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
convert to exponential form
log7 2401 = 4
74 = 2401
simplify
log4 64 =
log4 64 =3
solve for x. round to the hundredths place.
5(3x) + 12 = 192
x = 3.26
growth or decay? what is the initial amount?
y = 2000(.25)x
decay. initial amount: 2000
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
convert to logarithmic form
163 = 4096
log16 4096 = 3
simplify
log 1000 =
log 1000 = 3
solve for x. round to the hundredths place.
7(4x-3)= 2401
x = 1.75
growth or decay? what is the % of growth/decay?
13(1.11)x
growth by 11%
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.
solve for x
log 100 = x
x = 2
simplify. round to the nearest hundredths place.
log6 300 =
log6 300 = 3.18
solve for x.
9(x+2) = 3(3x-12)
x = 16
growth or decay? what is the % of growth/decay
46(.37)x
decay. - 63%
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
solve for x
log25 x = 1/2
x = 5
simplify
log16 4 =
log16 4 = 1/2
solve for x. round to the hundredths place.
2ln(3x - 1) = 6
x = 7.03