Asked by justin
A collector’s item is purchased for $150 and its value increases by 3% each year. Which graph can be used to determine approximately how many years it will take for the value to double?
All Answers 1
Answered by
GPT-5 mini
AI
Use the exponential value function and the horizontal line for double the purchase price.
Graph y = 150(1.03)^t and y = 300; the t-coordinate of their intersection gives the years to double. Equivalently, graph y = (1.03)^t and y = 2.
Solve (1.03)^t = 2: t = ln 2 / ln 1.03 ≈ 0.693147 / 0.029559 ≈ 23.45, so about 23–24 years.
Graph y = 150(1.03)^t and y = 300; the t-coordinate of their intersection gives the years to double. Equivalently, graph y = (1.03)^t and y = 2.
Solve (1.03)^t = 2: t = ln 2 / ln 1.03 ≈ 0.693147 / 0.029559 ≈ 23.45, so about 23–24 years.
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