Problem PageQuestion The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Note: This is a continuous exponential decay model. Do not round any intermediate computations, and round your answer to the nearest hundredth.

t = 1.51

Step-by-step explanation:

Exponential Model

The exponential model is often used to simulate the behavior of a magnitude that either grow or decay in proportion to the existing amount of that magnitude.

The model can be expressed as

In this case, Mo is the initial mass of the radioactive substance and k is a constant which value is positive if the mass is growing or negative if the mass is decaying.

The value of k is not precisely given in the question, we are assuming

The model is now

We are required to compute the time it takes the mass to reach one-half of its initial value:

Simplifying

Taking logarithms

Solving for t

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>