Question

The half-life of Mathium is 23 days. A 15 g sample of the element is monitored over time.

a) Write an equation that models the mass of Mathium remaining over time. Define variables clearly.
b) Determine the number of days it would take for there to be 1.05 g of Mathium left.

A. a) M(t) = 15 ⋅ (1/2)^(t/23), b) 40 days

B. a) M(t) = 15 ⋅ (1/2)^(t/23), b) 20 days

C. a) M(t) = 15 ⋅ e^(⁻t/23), b) 40 days

D. a) M(t) = 15 ⋅ e^(⁻t/23), b) 20 days

Answer 1

The equation that models the mass of Mathium remaining over time is M(t) = 15 ⋅ (1/2)^(t/23). It would take approximately 40 days for there to be 1.05 g of Mathium left.

Step-by-step explanation:

a) The equation that models the mass of Mathium remaining over time is M(t) = 15 ⋅ (1/2)^(t/23), where M(t) represents the mass of Mathium remaining at time t. In this equation, the variable t represents the time elapsed in days. The initial mass of Mathium is 15 g.

b) To determine the number of days it would take for there to be 1.05 g of Mathium left, we can substitute M(t) with 1.05 g in the equation and solve for t. The equation becomes 1.05 = 15 ⋅ (1/2)^(t/23). By solving this equation, we find that it would take approximately 40 days for there to be 1.05 g of Mathium left.