I'm a total noob and need help with this, I don't understand it at all. I need to find out the percentage change using the 2 numbers for each question, some have increased some have decreased.
Calculate the percentage (%) change in mass of carbon in the
atmospheric 662 becomes 850
soil and detritus 1700 becomes 1460
plant biomass 600 becomes 530
surface ocean reservoirs 918 becomes 1000
A change in percentage depends on the ratio $\frac{\text{after}}{\text{before}}$. The concrete formula would be $$\text{change in percent} = 100 \cdot \Big(\frac{\text{after}-\text{before}}{\text{before}}\Big)$$ Where $\text{after}-\text{before}$ is the change (with sign). This can be rewritten to $$\text{change in percent} = 100 \cdot \Big(\frac{\text{after}}{\text{before}} - 1\Big)$$ For example starting with $100$ and ending with $90$ you get a change percentage of $100\cdot (\frac{90}{100}-1) = 100\cdot (0.9 - 1) = 100\cdot(-0.1) = -10$.
A last example: Start at $123$ (before) and end at $234$ (after): $$100\cdot(\frac{234}{123} - 1) \approx 100\cdot(1.902 - 1) = 100\cdot 0.902 = 90.2 $$
Working out the formula if you know how to compute $x$ percent of a number: We will write the percentage directly as a number here. $x = 0.1 = 10\%$ for example.
To compute $x$ percent of a number $n$, we just compute $n\cdot x$. If we want to compute a new number $m$ wich is the old number increased by $x$ percent, this is then $$m = n + n\cdot x = n\cdot(1+x)\tag1$$ In the same way we could decrease using $m=n-n\cdot x = n\cdot(1-x)$. If we view $x$ as a signed percentage, for example $x = -0.1$ for a $10\%$ decrease, we can use the formula $(1)$ in both cases. Now we want to find $x$ given $n$ and $m$ in the assignment:
$$m = n\cdot (1+x)\\ \Leftrightarrow \frac mn = 1+x\\ \Leftrightarrow x = \frac mn - 1$$
Now since we want $x$ as a percentage number instead, we have to multiply the result by $100$ again: $$x[\%] = 100 \cdot x = 100\cdot \Big( \frac mn - 1 \Big )$$ Above $n$ was labelled $\text{before}$ and $m$ was labelled $\text{after}$.