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Q3. U235 is a radioactive isotope used in a nuclear propulsion system.

It decays into lead according to the law:

m = m₀ e^kt Where m_0 the original mass of U235 present and m is the mass present after t years.

The time taken for half of the isotope to decay is 7.04 × 10⁸ years.

(a) Determine EACH of the following:

(i) The value of K;

(ii) The time taken for a 100 mg sample of U235 to reduce to 99 mg.

(b) Solve the following equation for x;

4x × 10^2x+1 = 3^x+1