A colony of bacteria is growing at a rate of 0.2 times its mass. Here time is measured in hours and mass in grams. The mass of t
he bacteria is growing at a rate of 4 grams per hour after 3 hours. Write down the differential equation the mass of the bacteria, m, satisfies:
1 answer:
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Answer:
D
Step-by-step explanation:
So we have the equation:
And we want to find out which of the answer choices is <em>not</em> equivalent.
Thus, let's go through each of the choices.
A)
We have:
This is correct.
Our original equation can be written as:
And if we multiply straight across:
We'll get choice A. So choice A is correct.
B)
We have:
This is also correct.
From our original equation:
If we multiply the first term together:
We'll get choice B. So, choice B is correct.
C)
We have:
This is correct as well.
If we reduce 1/2 to decimal form and add the operations within the parentheses in the original equation, we will get:
So, C is also correct.
D)
We have:
Note that this is not correct.
This attempted to use the distributive property. However, the distribute property does <em>not work</em> for multiplication. For instance:
However:
So, choice D is not equivalent.
So choice D is our answer :)
If we evaluate it, we will get 30, in contrast to the 60 of the others.