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Charging a Battery The rate at which a battery charges is slower the closer the battery is to its maximum charge C0. The time (in hours) required to charge a fully discharged battery to a charge C is given by
where k is a positive constant that depends on the battery. For a certain battery, k = 0.25. If this battery is fully discharged, how long will it take to charge to 90% of its maximum charge C0?
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Chapter 4 Solutions
Precalculus: Mathematics for Calculus (Standalone Book)
- Charging a Battery The rate at which a battery change is slower the closer the battery is to its maximum change c The time (in hours ) required to change a fully discharged battery to a charge C is given by t=In(1cc) Where k is a positive constant that depends on the battery. For a certain battery, k=0.25 . If this battery is fully discharged, how long will it take to change to 90% of its maximum charge c ?arrow_forwardThe Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, the light is absorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensity I at depth x is given by the Beer-Lambert Law: I=I0ekx where I0 is the light intensity at the surface and k is a constant that depends on the murkiness of the water see page 402. A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. Light intensity decreases exponentially with depth. Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the murkiness constant k for this lake? Hint: If your calculator gives you a function of the form I=abx, convert this to the form you want using the identities bx=eln(bx)=exlnb. See Example 1b. Make a scatter plot of the data, and graph the function that you found in part a on your scatter plot. If the light intensity drops below 0.15 lumen lm, a certain species of algae cant survive because photosynthesis is impossible. Use your model from part a to determine the depth below which there is insufficient light to support this algae. Depth ft Light intensity lm Depth ft Light intensity lm 5 10 15 20 13.0 7.6 4.5 2.7 25 30 35 40 1.8 1.1 0.5 0.3arrow_forwardThe Beer-Lambert Law As sunlight passes through the waters of lakes and oceans, thelight isabsorbed, and the deeper it penetrates, the more its intensity diminishes. The light intensityI at depth x is given by the Beer-Lambert Law: I=I0ekx Where I0 the light intensity at the surface and k isis a constant that depends on the murkiness of the water (see page 402). A biologist uses a photometer to investigate light penetration in a northern lake, obtaining the data in the table. (a) Use a graphing calculator to find an exponential function of the form given by the Beer-Lambert Law to model these data. What is the light intensity I0 at the surface on this day, and what is the “murkiness” constant kfor this lake?(Hint: if your calculator gives you a function of the form I=abx .convert this to the form you want using the identities bx=eIn(bx)=exInb . See Example 1(b).) (b) Make a scatter plot of the data, and graph the function that you found in part (a) on your scatter plot. (c) If the intensity drops below 0.15 lumen (lm) , a certain species of algae can’t survive because photosynthesis is impossible. Use your model from part (a) to determine the depth below which there is insufficient light to support this algae.arrow_forward
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