Math

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How do I solve this if there is no equation to this

1. The population of the bacteria in a Petri dish increases by a factor of 10 every 10 hour. If there are initally 20 bacteria in the dish, how long will it take before the population increases to 60,000 to the nearest tenth of an hour?

a) 3000.0 h
b) 300.0 h
c) 4.8 h
d) 3.5 h

2. A certain radioactive isotope has a half life of 5 years. If a sample has 120 grams of radioactive material, what equation could be used to determine the amount of material remaining (y) after x years.

a) y=120x(1/2)^5x
b) y=60^5x
c) y=120x5^1/2x
d) y=1/2x120^5x

• Math -

1.
doubling time is 10

amount = 20(10)^(x/10)
so ...
60000= 20(10)^(x/10)
3000 = 10^(x/10)
log both sides
log 3000 = log 10^(x/10)
x/10 = log 3000
x = 10log3000 = 34.8 hrs.

proof
at end of 10 hours; 20(10) = 200
at the end of 20 hrs = 200(10) = 2000
at the end of 30 hrs = 2000(10) = 20000
at the end of 40 hrs = 20000(10) = 200000
so the time must have been between 30 and 40 hours
amount = 20(10)^34.8/10)
= 20(10)^3.48
= 60399

none of your choices are correct.

2.
amount = 120(1/2)^(x/5)

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