Question

A bacterial culture, growing exponentially,
Increases from 100 to 400 grams in 10 hours.
How much was present after 3 hours?​

Answer 1

Answer:

490

Step-by-step explanation:

in 10 hours it inctreases by 300 grams

thus, in 1 hour it increases by 300/10=30 grams

thus in 3 hours it increases by 3*30=90 grams

thus after 3 hours , 400+90=490 grams will be present

Answer 2

There are 152 grams of bacteria after 3 hours.

Step-by-step explanation:

Since we have given that

Initial bacteria = 100

After 10 hours,

number of bacteria = 400

Since it increases exponentially, so, our equation becomes,

$Amount=Ab^x\\\\400=100b^{10}\\\\4=b^{10}\\\\\ln 4=10\ln b\\\\\dfrac{\ln 4}{10}=\ln b\\\\b=e^{0.139}=1.15$

Now, we need to find the bacteria present after 3 hours.

So, it becomes,

$Amount=100(1.15)^3\\\\Amount =152\ grams$

Hence, there are 152 grams of bacteria after 3 hours.

# learn more:

A bacterial population increases from 100 to 100,000,000 in 15 hours. What is the generation time of this culture.

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