A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work. please help

The half-life of this radioactive substance is of 8.6 months.

Step-by-step explanation:

Exponential decay of an amount:

The equation that models an amount after t units of time, subject to exponential decay, is given by:

In which A(0) is the initial amount and r is the decay rate, as a decimal.

A radioactive substance decays to 30% of its original mass in 15 months.

This means that . We use this to find 1 - r.

So

Determine the half-life of this radioactive substance to the nearest tenth.

This is t for which A(t) = 0.5A(0). So

The half-life of this radioactive substance is of 8.6 months.

the correct answer is 5

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).