Question

alaskas summer growing season creates some of the most extreme photosynthesis conditions on earth. from may through august, alaskan farmers experience nearly 20 hours of daylight due to the \midnight sun\ phenomenon. this extended light exposure allows giant pumpkins to grow to massive sizes, sometimes exceeding 1,000 pounds. meanwhile, hawaii receives 12 - 13 hours of daylight year - round due to its location near the equator. while hawaiian plants enjoy warm temperatures and consistent conditions, they receive significantly less total daily light energy for photosynthesis. a typical hawaiian pumpkin averages around 20 pounds, despite having ideal growing temperatures. over a 90 - day growing season, how many total hours of sunlight does each location receive? despite the whole of pumpkins being edible we typically consume only 70 percent of a pumpkin. how many kilograms of an average alaskan pumpkin would you expect to be eaten based on this? (1 pound =.45 kg) pumpkins can be fermented, a process where the plants consume their sugar without the presence of oxygen. a fermenting pumpkin has an initial glucose mass of 7.7 kilograms and after fermenting for 2 weeks has a final glucose mass of 2.4 kilograms. what percentage of the pumpkin was fermented? what is the rate of glucose fermented in grams/hour?

Explanation:

Step1: Calculate sunlight hours for each location

For Alaska, with 20 hours of daylight per day over 90 - day season. Total sunlight hours = 20×90 = 1800 hours.
For Hawaii, assume 12 hours of daylight per day (average for equatorial - like regions) over 90 - day season. Total sunlight hours = 12×90 = 1080 hours.

Step2: Calculate eaten mass of Alaskan pumpkin

An average Alaskan pumpkin is 1000 pounds (assumed from context as giant). 1 pound = 0.45 kg, so mass of Alaskan pumpkin = 1000×0.45 = 450 kg. We consume 70% of it. Eaten mass = 450×0.7 = 315 kg.

Step3: Calculate percentage of fermented pumpkin

Initial glucose mass $m_1$ = 7.7 kg, final glucose mass $m_2$ = 2.4 kg. Mass fermented $m = m_1 - m_2=7.7 - 2.4 = 5.3$ kg. Percentage fermented = $\frac{5.3}{7.7}\times100\%\approx68.83\%$.

Step4: Calculate rate of glucose fermented

2 weeks = 2×7×24 = 336 hours. Mass fermented is 5.3 kg = 5300 g. Rate of glucose fermented = $\frac{5300}{336}\approx15.77$ g/hour.

Answer:

• Total sunlight hours in Alaska: 1800 hours
• Total sunlight hours in Hawaii: 1080 hours
• Eaten mass of Alaskan pumpkin: 315 kg
• Percentage of fermented pumpkin: Approximately 68.83%
• Rate of glucose fermented: Approximately 15.77 g/hour