Logarithms and Exponents Applications Word Problems
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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
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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 ...
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