Which metric unit of weight is appropriate?

Learning Objectives Calculate the final mass of a substance undergoing exponential growth or decay. Convert fluently between metric units of weight, including kilograms, grams, milligrams, and micrograms. Analyze the result of an exponential function to determine its order of magnitude. Select the most appropriate metric unit of weight to express a very large or very small calculated value. Justify their choice of a metric unit based on the context of an exponential growth or decay problem. Interpret real-world scenarios involving exponential change in mass, such as bacterial growth or radioactive decay. Ever wonder how scientists measure the weight of a single bacterium that doubles every hour? 🦠 How would you write that number down after a full day of growth? In this les...

TermDefinitionExample Exponential GrowthA pattern where a quantity increases by a fixed percentage over equal time intervals. The growth rate becomes more rapid as the quantity increases.A bacterial culture starts at 1 milligram and its mass doubles every hour. After 1 hour it's 2 mg, after 2 hours it's 4 mg, after 3 hours it's 8 mg, and so on. Exponential DecayA pattern where a quantity decreases by a fixed percentage over equal time intervals. The rate of decrease slows down as the quantity gets smaller.A 100-gram sample of a radioactive substance has a half-life of one year. After 1 year, 50 g remain; after 2 years, 25 g remain; after 3 years, 12.5 g remain. Metric Prefixes for WeightSymbols used before the base unit 'gram' (g) to represent powers of 10, making...

Exponential Growth Formula W(t) = W_0 (1 + r)^t Calculates the final weight, W(t), after 't' time periods. W_0 is the initial weight, and 'r' is the growth rate per period (as a decimal). Exponential Decay Formula W(t) = W_0 (1 - r)^t Calculates the final weight, W(t), after 't' time periods. W_0 is the initial weight, and 'r' is the decay rate per period (as a decimal). For half-life problems, the base (1-r) is simply 0.5. Metric Conversion Hierarchy 1 kg = 1000 g; 1 g = 1000 mg; 1 mg = 1000 µg To convert from a larger unit to a smaller unit (e.g., g to mg), multiply by 1000. To convert from a smaller unit to a larger unit (e.g., mg to g), divide by 1000.