Application of calculus to the physical world (1 Viewer)

[Kiriii cx]

Helppppp….. I got stuck on this question, I'm not able to get the answer that is in the back of the book

a formula for the rate of change in population of a certain species of animal is given by P=200+1600(e^-kt). If the population reduces to half after 56 years, find how long it would take to reduce to a quarter of the original population

Answer: 125.7 years

Appreciate all the help c;

 

[fan96]

If .

Substituting in ,



Refreshing the equation,



And solving for when gives .

 

[Kiriii cx]

Yusss, Thank you so much, I thought we can use 1600 as the initial value XD.

I got another question from the same kind.

A saucepan of water is brought nearly to the boil. if the temperature reaches 95°C and cools down to 75% of this temperature after 2.5 minutes, find how long it will take for the water to cool down to 30°C, if room temperature is a constant 25°C.


Answer is 16
mins

 

[fan96]

First start with



Given that the room temperature is 25, .



Looking at the RHS: as , shrinks to zero and so the second term approaches zero.

Therefore .

Now we have



Substitute to find .

Then substitute to find .

The rest should be simple.