Rate is directly proportional word problem

The video tutorial focuses on solving a word problem involving exponential growth. It begins by identifying key information, such as initial and final values, and explains the concept of rate of proportionality. The tutorial then demonstrates how to solve for the constant K in the exponential growth equation. Finally, it calculates the growth rate when the population reaches 3000, using the previously determined value of K.

What does the equation Y = CE^rt represent in the context of exponential growth?

• Y is the time, C is the rate, r is the final amount, and t is the initial amount.

• Y is the initial amount, C is the final amount, r is the rate, and t is time.

• Y is the final amount, C is the initial amount, r is the rate, and t is time.

• Y is the rate, C is the time, r is the initial amount, and t is the final amount.

How do you isolate the rate of proportionality (K) in the equation 600 = 400 * E^(3K)?

• Divide both sides by 400 and then take the natural logarithm.

• Multiply both sides by 400 and then take the natural logarithm.

• Subtract 400 from both sides and then take the natural logarithm.

• Add 400 to both sides and then take the natural logarithm.

What is the value of K if the equation is 600 = 400 * E^(3K)?

• K = 3 * ln(4)

• K = ln(4)

• K = 1/3 * ln(4)

• K = 1/3 * ln(2)

When the population is 3000, how do you calculate the rate of increase using the formula dP/dt = K * P?

• Subtract 3000 from K.

• Add 3000 to K.

• Divide 3000 by K.

• Multiply 3000 by K.

What is the result of multiplying 3000 by 1/3 in the context of calculating dP/dt?

• 1000

• 300

• 3000

• 9000