How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function a(t) = 350e-0.169t, where t is the time in years? round your answer to the nearest hundredth year.

4.101 yrs

Step-by-step explanation:

Given that a sample of radioactive substance to decay has the following exponential function.

where t= no of years lapsed

When t=0 i.e. initially we have population as

When it becomes half we have

=

Taking log to base e we have

In approximately 4.101 years the population decays to half

Step-by-step explanation:

The image attached shows those vectors.

Now, assuming that each vector represents each side of the triangle, we can classify it by finding the module of each vector with the following formula.

Vector 1.

Vector 2.

As you can see, the length of each vector (side) is the same, but it's not enough information to it's an equilateral triangle, it could be a right triangle.

Notice that the given points has the same absolute values, but with changes. Specifically, the relation between the given points is

, which is a rotation of 90°.

All this means that those sides are perpendicular to each other, due to the relation of those vectors.

Therefore, the triangle is right, because it has a right angle.