Final answer:
The function to model the growth of a substance at a 35% hourly rate, starting at 5040 grams, is an exponential growth function: Mass(t) = 5040 × (1 + 0.35)^t.
Step-by-step explanation:
The function that represents the growth of a substance at a rate of 35% per hour, starting with an initial mass of 5040 grams, follows the principle of exponential growth. To model this, we can use the exponential growth formula:
Mass(t) = initial_mass × (1 + growth_rate)^t
Where initial_mass is 5040 grams, growth_rate is 0.35 (corresponding to 35%), and t represents the time in hours.
Therefore, the function is:
Mass(t) = 5040 × (1 + 0.35)^t
This equation implies that every hour, the mass will increase by 35% of the mass at the start of that hour. This type of growth is common in populations of organisms, such as bacteria, under ideal conditions, and can also apply to other contexts like finance and physical sciences.