How to find the constant k of rate proportionality

The video tutorial explains the concept of rate proportionality, where the rate of change is proportional to the current amount. It addresses the problem of finding the constant K when the amount triples every 11 hours. The instructor discusses the challenge of unknown initial and final values and demonstrates how to solve for K using examples. The process is simplified by using logarithms, and the tutorial concludes with a recap and final example to reinforce the learning.

What is the relationship between the rate of change and the current amount in exponential growth?

• The rate of change is unrelated to the current amount.

• The rate of change is constant regardless of the current amount.

• The rate of change is directly proportional to the current amount.

• The rate of change is inversely proportional to the current amount.

When solving for the constant K, why can we assume any initial and final values?

• Because the constant K changes with different initial values.

• Because the constant K remains the same as long as the final value is triple the initial value.

• Because the final value must always be double the initial value.

• Because the initial and final values do not affect the rate of change.

What is the first step in isolating K in the equation for exponential growth?

• Subtract the initial value from both sides.

• Multiply both sides by the initial value.

• Divide both sides by the final value.

• Take the natural logarithm of both sides.

How is the constant K calculated when the amount triples every 11 hours?

• K = (ln 5) / 11

• K = (ln 2) / 11

• K = (ln 4) / 11

• K = (ln 3) / 11

What happens to the value of K if the initial and final values are changed but the final value is still triple the initial?

• The value of K increases.

• The value of K decreases.

• The value of K remains the same.

• The value of K becomes zero.