Track / Stage 4 / 138 of 340 #398 of 1964

Problem 398

AMC 12 late, AIME early

Algebra Difficulty 4.7 Find the answer

In the formula $l=l_{0}(1+\alpha l)$ , the letter $l_{0}$ represents the length of the metal rod at temperature $t=0, t$ the temperature, $\alpha$ a constant number (so-called coefficient of linear expansion). What function of the variable $t$ is $l$ ? What specific value does the constant $\alpha$ have?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

339. $t$ is a linear function of $l$ ; $\alpha$ is the increment in the length of the rod by 1 centimeter when the temperature is raised from $0^{\circ}$ to $1^{\circ} \mathrm{C}$ .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.