1. Solve the exponential equation by expressing each side as a power of the same base and then equating exponents. 6 x = 216 x = 3
2. Solve the exponential equation. Express the solution in terms of natural logarithms. Then use a calculator to obtain a decimal approximation for the solution. ex = 22.8 x= ~3.12676
3. Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. Log7 x = 2 x=49
4. Solve the logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expression. Give the exact answer. Log (x + 16) = log x + log 16 x=16/15
5. Modeling Population: The population of the world has grown rapidly during the past century. As a result, heavy demands have been made on the world's resources. Exponential functions and equations are often used to model this rapid growth, and logarithms are used to model slower growth. The formula models the population of a US state, A, in millions, t years after 2000.
a. What was the population in 2000? 16.6 million
b. When will the population of the state reach 23.3 million? February, 2006
6. The goal of our financial security depends on understanding how money in savings accounts grows in remarkable ways as a result of compound interest. Compound interest is computed on your original investment as well as on any accumulated interest. Complete the table for a savings account subject to 4 compounding periods yearly.
Amount Invested | Number of Compounding Periods | Annual Interest Rate | Accumulated Amount | Time t in Years |
$15,500 | 4 | 5.75% | $30,000 | |
7. Cell division is the growth process of many living organisms such as amoebas, plants, and human skin cells. Based on an ideal situation in which no cells die and no by-products are produced, the number of cells present at a given time follows... [continues]
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