Question
My fruit is about 1 inch long and the very bottom of the
fruit is black, also the leaves are starting to curl.
the plant is in a pot which drains and in sunlight 80% of
the day.

Answer
When peppers or tomatoes rot prematurely on the bottom of the fruit, it is usually an indication of blossom-end rot. This condition is caused by inconsistent watering and/or a lack of calcium in the soil.

When plants are watered too shallow, the roots reach for the surface causing stress and poor nutrient intake.  By the same token, when plants are given too much water, the roots are deprived of oxygen and cannot absorb specific nutrients that are not as concentrated as others.  Calcium is one of these nutrients.

Most soils in the US are very low in calcium.  To counter this problem, you can add crushed eggshells to the soil or you can spray the plants with a solution of 1 tbs. of Epsom salts per gallon of water. Although Epsom salts are comprised primarily of magnesium, it has been proven that the plants will draw more calcium and other vital nutrients more efficiently when sprayed with Epsom salts. I add one or two tablespoons into each planting hole in the spring, and I seldom experience problems with blossom-end rot on either my tomatoes or peppers.

Finally, if you're not getting at least 1.5" of rain per week, make sure you water the soil deeply once or twice per week.  This will force the roots to grow deeper where lesser concentrated nutrients are more readily available. You should also mulch the plants heavily with dried grass clippings or straw to help retain moisture.

I hope this answered your question. Please write again if I can ever be of assistance.

Regards,

Mike