# Logarithms and Exponents Applications Word Problems

1. Complete table for savings in which interest is compounded continously.

Initial investment Annual rate Time to double total

$1000 ? ? $2281.88

2. Complete table for radioactive isotope

Isotope Half-life(years) Initial quantity Amt after 1000 years

5715 ? 3.5g

3. The population of P of a city is given by P= 105300 e^0.015t, where t represents the year with t=0 corresponding to 2000. Sketch the graph of this equation.According to this model, in which year will city have population of 150,000?

4. The management at a factory has found that the maximum number of units a worker can produce in a day is 30. the leaning curve for the number of units N produced per day after a new employee has worked t days is given by

After 20 days, a worker produced 19 units in 1 day.

a. Find the learning curve for this worker (first hand the value of k)

b. How many days should pass before this worker is producing 25 units/day?

5. Plot the complex number : 1 - 2i

6. Evaluate expression. Round 3 places

7. Sketch graph of rational function as sketching aids, check for intercepts, symmetry, vertical asymptotes, and horizontal asymptotes

i. ii.

8. approximal real zeros with zoom and trace

Â© BrainMass Inc. brainmass.com December 15, 2022, 5:31 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/logarithms-exponents-applications-word-problems-88311

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

1. Complete table for savings in which interest is compounded continously.

Initial investment Annual rate Time to double total

$1000 ? ? $2281.88

Solution: There is missing information in this problem. The formula for continuous compound interest is A = P exp(rt) where P is the principal, r is the annual interest rate, t is the time in years, and A is the amount after time t. All we know is A = $2281.88 and P = $1000; so exp(rt) = P/A or rt = ln(P/A).

If we knew r, we could solve for the time to double, d, by solving the equation

2P = A. Since exp(rt) = P/A, this means exp(rt) = 1/2 , or rt = ln(1/2), so d = t = ln(1/2)/r.

2. Complete table for radioactive isotope

Isotope Half-life(years) Initial quantity Amt after 1000 years

5715 ? 3.5g

Solution:

Radioactive substances decay exponentially. That is, the mass M after time t is given by the equation M = I exp(rt) , where r is a decay rate and negative, and I is the initial amount. The half-life ...

#### Solution Summary

Logarithms and Exponents Applications Word Problems are solved.