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Determining Solutions In Exercises 3-6, determine whether each x-value is a solution (or an approximate solution) of the equation.
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- ANSWER ALL THE QU A 200g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138 days, the amount of polonium left in the sample is half of the original amount. a) Write an equation that models the amount of Polonium b) What mass of Polonium-210 is left after 2 years? c) Determine how long it will take for the sample to reduce to 150g The University of McMaster undergraduate program is growing at a rate of 3% each year. The current enrollment is 12400. Determine when the enrollment will reach 13250. You have found an investment at the bank that pays 2.4% interest per year for 10 years. How much should you invest now so that you have $2000 at the end of the 10 years?arrow_forward3. Solving Equations Solve each equation using the method of your choice. Give each solution in two forms: exact and rounded to the nearest hundredth. Be sure to fully justify your response by showing all work and/or explaining your reasoning in detail. a) 2e²x + 5e* - 3 = 0 (Hint: let u = e*, and factor the resulting quadratic equation). + 5) = 2log (3) b) log(x - 2) + log(xarrow_forward9. A scientist isolates a culture of 100 bacteria. The amount of bacteria in the culture doubles every 2 hours. The sample can be represented by the exponential equation y = 100 - 23. Solve the equation for t.arrow_forward
- Sound intensity Refer to Exercise 61. A sound intensity level of 140 decibels produces pain in the average human ear. Approximately how many times greater than I, must I be in order for a to reach this level?arrow_forwardsolve 4arrow_forwardSolve r? - 4.x + 6y = log x² 4.r + 6y = log x?arrow_forward
- The population of a small island is growing at a rate that is proportional to its size. In 2016, the island's population is 1400, and in 2020, the island's population is 1600. What will the island's population be in 2030? O = 2234 There is not enough information to answer this. O = 2553 O = 1955arrow_forwardPhysicists using the radioactivity equation y = yo e - kt call the number 1 the mean life of a radioactive nucleus. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t=. Thus, the mean life of a k nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... - kt If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). C. Set y(t) equal to 0.05y, and solve for t. D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo - kt e = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 x (Round to three decimal places as needed.) Since this value is approximately equal to then 95% of a sample will…arrow_forwardBoth pleasearrow_forward
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