Increase the worth of my apple by 15% for every 1+ pear that I have

Question

Apples: 1
Apple Value: 2500
Pears: lowest = 1, highest = 10

If I have 1 apple and my apple is worth 2500 if I have 1 pear, how can I calculate the value of my apple if I have X pears, at a maximum of 10 pears and a minimum of 1 pear, where 1 pear represents 100% value and 10 pears represents an increase of that value by 150%?

Apple Worth = 2500 * (1+((pears*15)/100))

This formula sort of works. The problem here is that if I have 1 pear, the value becomes 2500 * 1.15 = 2875 which is incorrect, as the value of my apple always is 100% of it's original value if I have at least 1 pear (pear count can never go below 1).

What am I missing here?

Edit:

Some clarification.

2500 = 1p = 100% (do not add 0.15 until p > 1)

2875 = 2p = 115%
3250 = 3p = 130%
3625 = 4p = 145%
4000 = 5p = 160%
4375 = 6p = 175%
4750 = 7p = 190%
5125 = 8p = 205%
5500 = 9p = 220%

5875 = 10p = 235% 

6250 = 11p = 250% (this is what 10p should be)

At 1 pear, my apple is worth 100% of it's original value, so this means that unless I have more than 1 pear, I can't add 0.15% per pear. The first pear is, in other words, not worth 0.15%, but rather 0%. This also means that the 10th pear should be 250% and not 235%.

Answer 1

You want the apple's value to be $2500$ at $1$ pear. There are two different ways to describe the linear growth of the apple's value for additional pears, depending on which of two conditions you want to impose.

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If you want the value to increase linearly for each additional pear, until it reaches $6250$ at $10$ pears, then we can calculate the amount by which the value must increase, per pear.

Nine linear increases must make up the difference, so the amount by which the apple's value increases per pear must be $$\frac{6250-2500}{9} = 416.\overline{6}$$

The apple's value at $p$ pears for $1 \leq p \leq 10$, is then $$2083.\overline{3} +416.\overline{6}p$$

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If, instead, you want the value to increase by $15\%$ of $2500$, or $375$, for each additional pear, then we have a different result:

At $p$ pears, for $1 \leq p \leq 10$, you want the value of the apple to be $$2500+(p-1)(0.15)(2500) = \boxed{2125 + 375p\,}$$

This means that at $10$ pears, the value of the apple is $5875$.

Answer 2

The formula is \begin{eqnarray*} \text{Apple Value} = 2500 \left( \frac{ 85+15p}{100} \right) . \end{eqnarray*} where $p$ is the number of pears.