rules of exponents in Algebra Toolkit C.1 on page T47 1-8 Solve the equation for
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rules of exponents in Algebra Toolkit C.1 on page T47 1-8 Solve the equation for 1.-16 4,2' = 486 27 9-12 Solve the equation for x; express your answer correct to two 10, 2r'-9 11. x"-7.35 12. 3 34.12 ercises TS Fundamentals 1. The bacteria population in a certain culture grows exponentially (a) If the 20-minute growth factor is a, then the one-hour growth factor is (b) If the five-hour growth factor is b, then the one-hour growth factor is (e) If the half-life of a radioactive element is h years, then the yearly decay factor is 2. In the compound interest ormula 4thers P.rn,andrs for " and , respectively, and A (r) stands for Think About It 3. Biologists often report population growth rates in fixed time periods such as one hour one day, one year, and so on. What are some of the advantages of this type of reporting (as opposed to reporting 38-minute growth rates or nine-day growth rates)? 4-The rate of decay of a radioactive element is usually expressed in terns of its half-life. Why do you think this is? How is this more useful than reporting yearly decay rates? 5-6 A population P starts at 2000, and four years later the population reaches the given number (i) Find the four-year growth or decay factor (ii) Find the annual growth or decay factor. 5. (a) 8000 6. (a) 6000 (c) 1500 (d) 1200 (b) 20,000 (b) 3000 (c) 800 (d) 400 The bacteria population in a certain culture grows exponentially. Find the one-hour growth rate if 7-10 8. the 15-minute growth rate is 0.09. 7. the 10-minute growth rate is 0.02. 10the four-hour growth rate is 72%. gs, the three-hour growth rate is 57%.Explanation / Answer
Established formulas for a population at time t if the population has a constant absolute ( P(t) = P(0) + P(t)t ) or relative ( P(t) = P(0)(1+ r) t ) growth rate
Since Population is usually considered a exponential growth phenomenon so options C and D are not correct.
Next we need to identify which of the two fits in the exponential graph
6000= 2000 (1+r)
3000 = 2000 (1+r)
for option a ) r= 200% and for option b) r = 50%
Since option a ) depicts a more close exponential curve , hence it is the correct option
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