$\frac{dA}{dt}}=0.5\times A\times (1-{\displaystyle \frac{A}{100}})-10$

with $A(0)=70$ and we want to use Euler's method to get an approximate value for $A(10)$, with a step size of 1.

So the answer sheet says you basically have to use $\text{Ans}+0.5\times \text{Ans}\times (1-{\displaystyle \frac{\text{Ans}}{100}})-10$ with the first Ans being 70, and then of course repeat 10 times.

But I'm wondering, doesn't this actually give you $\frac{dA(10)}{dt}$? How is this a correct method?

with $A(0)=70$ and we want to use Euler's method to get an approximate value for $A(10)$, with a step size of 1.

So the answer sheet says you basically have to use $\text{Ans}+0.5\times \text{Ans}\times (1-{\displaystyle \frac{\text{Ans}}{100}})-10$ with the first Ans being 70, and then of course repeat 10 times.

But I'm wondering, doesn't this actually give you $\frac{dA(10)}{dt}$? How is this a correct method?