Question 1190048: The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab. The doubling time for this substance was observed to be 14 days. There were 9.3 mg of the substance present at the beginning of the study.
(a) Let t be the time (in days) since the beginning of the study, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
(b) How much will be present in 16 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
The mass of a substance, which follows a continuous exponential growth model, is being studied in a lab.
The doubling time for this substance was observed to be 14 days.
There were 9.3 mg of the substance present at the beginning of the study.
(a) Let t be the time (in days) since the beginning of the study, and let
y be the amount of the substance at time t.
Write a formula relating y to t.
Use exact expressions to fill in the missing parts of the formula.
Do not use approximations.
(b) How much will be present in 16 days?
Do not round any intermediate computations, and round your
answer to the nearest tenth
~~~~~~~~~~~~~~~~~
The formula is
y = 9.3*2^(t/14).
Notice that 9.3 is the initial amount at the beginning (9.3 mg at t= 0).
The denominator "14" in the index of the exponential function is the doubling time of 14 minutes.
t is the current time in minutes.
To calculate the mass at t= 16 minutes, substitute t= 16 into the formula and compute.
Solved and explained.
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To see many other solved problems on exponential growth/decay, look into the lessons
- Population growth problems
- Radioactive decay problems
- Carbon dating problems
- Bacteria growth problems
- A medication decay in a human's body
- Problems on appreciated/depreciated values
- Inflation and Salary problems
in this site.
Consider these lessons as your handbook, textbook, guide, tutorials, and (free of charge) home teacher.
Learn the subject from there once and for all.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic "Logarithms".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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