Question

PLEASE HELP! THIS IS MY LAST QUESTION, BUT I DON'T KNOW HOW TO DO IT!

The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. A sample increases continuously at a relative rate of 7% per day. Find the mass of the sample after six days if there were 552 grams of the substance present at the beginning of the study.
Do not round any intermediate computations, and round your answer to the nearest tenth.

Also, may you please explain how you got the answer, it would be very helpful because I don't understand how to solve this. Thank you!

Answer 1

864.3

Explanation:

Since the substance is increasing continuously at a relative rate of 7% per day, we can use the continuous exponential growth formula:

P(t) = P(0) * e^(rt)

where:

P(t) is the mass of the substance after "t" days

P(0) is the initial mass of the substance (552 grams in this case)

e is the mathematical constant e (approximately equal to 2.71828)

r is the relative growth rate (0.07 per day in this case)

Substituting the given values, we get:

P(t) = 552 * e^(0.07t)

To find the mass after 6 days, we can substitute t = 6:

P(6) = 552 * e^(0.07*6)

Using a calculator, we get:

P(6) ≈ 864.3 grams

Therefore, the mass of the substance after 6 days is approximately 864.3 grams rounded to the nearest tenth.