A-level maths help :(

Hey! I believe its because as t tends to infinity, the expression tends to 800/3. This is 266.6666... so the value can never reach 270.

Hello, I do get that but wouldn't that mean the denominator would be 4?

So what i would do is in the fraction divide each term by e^0.1t
After doing that, since the e^0.1t tends to infinity as t increases, the 1/ (e^0.1t) term you're left with must tend to 0. That means you only have 3 left at the bottom.
Did that make sense, cause i'm not sure if it did! otherwise I can try explain it again

That makes a lot more sense, thank you!

Hey! I believe its because as t tends to infinity, the expression tends to 800/3. This is 266.6666... so the value can never reach 270.

So what i would do is in the fraction divide each term by e^0.1t
After doing that, since the e^0.1t tends to infinity as t increases, the 1/ (e^0.1t) term you're left with must tend to 0. That means you only have 3 left at the bottom.
Did that make sense, cause i'm not sure if it did! otherwise I can try explain it again

That makes a lot more sense, thank you!

You need to be careful with that argument. Just because it tends to 800/3 at infinity doesn't mean there can't be a value "before infinity" where it does hit 270.



You can actually solve directly by setting P = 270 and rearranging. You will end up with the conclusion that $e^{0.1t} < 0$ which is a contradiction because e^x can never be negative for any real number x