Worksheet 7-5B Applications of Exponential and Logarithmic Equations CC06
Solve each problem. Round to 3 decimal places if necessary.
1. 10x – 3 = 50 2. ex + 4 = 10 3. 2(10x) = 160
4. 3ex + 1 = 95 5. 102x – 9 = 40 6.
7. 2 log4 3 = log4 x 8. log3 5 – log3 x = log3 2 9. 1/3 log10 x = log10 3
The pH of a patient’s blood can be calculated using the Henderson-Hasselbach Formula:
pH = 6.1 +
where B is the concentration of bicarbonate and C is the concentration of carbonic acid. The normal pH is approximately 7.4.
10. A patient has a bicarbonate concentration of 24 and a carbonic concentration of 1.9. Find the pH of the patient’s blood.
11. A patient with a normal blood pH has a bicarbonate concentration of 24. Find the concentration of carbonic acid.
The amount in an account after t years (when compounding is continuous) is A = Pert, where r is the annual interest rate and P is the principal.
12. You deposit $1200 in an account that pays 5% interest. Find the amount in the account after 10 years if it is compounded continuously.
13. You deposit $2000 in an account that pays 3.5% interest. Find the amount in the account after 5 years, if it is compounded continuously.
The amount (N) of an element after t time periods is given by the half-life formula
where h is the half-life and N0 is the initial amount.
14. One isotope of chromium has a half-life of 20 hours. How much of a 100-gram sample is left after 100 hours?
15. How long would it take 80 grams of the chromium (half-life of 20 hours) to decay to 50 grams?
Evaluate (with a calculator). Round to three decimal places. Show your work.
16. log3 50 17. log5 56
18. log4 42 19. log6 73
20. log5 60 21. loga x