Final answer:
To find the exponential decay model for titanium-44 with a half-life of 63 years starting with 25 g, use the formula P(t) = 25(1/2)^(t/63), where t is the time in years.
Step-by-step explanation:
The student has asked for the exponential model of decay for titanium-44 which has a half-life of approximately 63 years. Since at t = 0 there are 25 g of the substance, we use the formula:
P(t) = P0(1/2)t/T
Where P(t) is the amount of substance at time t, P0 is the initial amount (25 g in this case), and T is the half-life of the substance (63 years). The model of decay for this substance would be:
P(t) = 25(1/2)t/63
This model is commonly used to describe various natural phenomena, such as radioactive decay, population decrease, cooling of a hot object, or the diminishing concentration of a substance over time.
The rate of decay (�k) is a crucial parameter; it determines how quickly the quantity decreases. A larger �k means faster decay, resulting in a steeper decline over time.