Metric units of length: word problems

Learning Objectives Identify the initial value, growth/decay factor, and time period in a word problem involving metric lengths. Model real-world scenarios of exponential growth or decay using the formula y = a(b)^x. Solve for the final length in an exponential word problem. Convert between common metric units of length (mm, cm, m, km) to answer a specific question. Interpret the solution of an exponential function within the context of a metric length word problem. Analyze how changes in the growth/decay factor affect the final outcome over time. If a piece of paper 0.1 mm thick could be folded 42 times, would it reach the moon? 🌕 Let's use exponential functions to find out! This tutorial connects the abstract power of exponential functions to tangible, real-world me...

TermDefinitionExample Exponential FunctionA function of the form y = a(b)^x, where 'a' is the non-zero initial value, 'b' is the growth/decay factor (b > 0 and b ≠ 1), and 'x' is the independent variable (often time or number of iterations).A plant's height, starting at 5 cm and doubling each week, can be modeled by H(w) = 5(2)^w, where w is the number of weeks. Initial Value (a)The starting amount or value at time zero (when x = 0). In our problems, this is the starting length.If a crack in a sidewalk starts at 2 mm long, the initial value 'a' is 2 mm. Growth Factor (b > 1)The constant multiplier by which a quantity increases over each time period. It is calculated as (1 + r), where 'r' is the growth rate as a decimal.If a vine...

Exponential Growth Formula y = a(1+r)^x Use this formula when a length is increasing by a fixed percentage 'r' (as a decimal) over 'x' time periods. 'a' is the initial length. Exponential Decay Formula y = a(1-r)^x Use this formula when a length is decreasing by a fixed percentage 'r' (as a decimal) over 'x' time periods. 'a' is the initial length. General Exponential Form y = a \cdot b^x A simplified form where 'b' is the growth factor (if b > 1) or decay factor (if 0 < b < 1). This is the most common form to use when the factor is given directly (e.g., 'doubles' or 'halves'). Metric Conversion Factors 1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm Use these convers...