When cane sugar is dissolved in water, it converts to invert sugar over a period of several hours

Question

When cane sugar is dissolved in water, it converts to invert sugar over a period of several hours. The percentage 𝑓(𝑡)of unconverted cane sugar at time 𝑡t (in hours) satisfies 𝑓′=−0.7𝑓

What percentage of cane sugar remains after  44 hours?

What percentage of cane sugar remains after  88 hours?

Answer 1

I'm curious if there might be a typo here, the numbers work out quite a bit nicer if it's ƒ' = -0.07ƒ.

But in either case. This is a differential equations problem. It can be easier to see what to do if you rewrite ƒ' as dƒ/dt instead.

Then you could work with:

df/dt = -0.7f

Which then can be converted as:

(1/f)df = -0.7dt

Integrate both sides and then you're on your way!