Question

The chemical element einsteinium-253 naturally loses its mass over time. A sample of an einsteinium-253 had an initial mass of 540 g when we measured it. The relationship the elapsed time T in months and the mass m(t) in grams left in the sample is modeled by the following function m(t)=540•(1/8)^t/2.05 complete the following sentence about the rate of change in the mass of the sample

Answer 1

The rate of change in the mass of the sample can be determined by finding the derivative of the function that models the relationship between elapsed time and mass.

Step-by-step explanation:

The rate of change in the mass of the sample can be determined by finding the derivative of the function that models the relationship between elapsed time and mass. To do this, we can use the power rule of differentiation. The derivative of the function m(t) = 540 * (1/8)^(t/2.05) is found by multiplying the constant term, 540, by the natural logarithm of the base, ln(1/8), and then multiplying it by the derivative of the exponent, (1/2.05). This gives us the equation:

m'(t) = 540 * ln(1/8) * (1/2.05) * (1/8)^(t/2.05-1)

By simplifying, we can express the derivative as:

m'(t) = -540 * ln(8) * (1/2.05) * (1/8)^(t/2.05-1)

Answer 2

Answer: The sample loses 7/8 of its mass every 2.05 months.

Step-by-step explanation:

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