## Calculus 8th Edition

Published by Cengage

# Chapter 1 - Functions and Limits - 1.2 Mathematical Models: A Catalog of Essential Functions - 1.2 Exercises - Page 34: 12

#### Answer

(a) The slope of T represents the rate of temperature change (change in temperature over time) (b) $12.50ºC$

#### Work Step by Step

(a) Slope = $\frac{rise}{run}$, which in this case is $\frac{T(temp)}{t(time)}$ as temperature lies on the y-axis. Thus, the slope represents the rate of temperature change, or the temperature change over time. (b) Years Since 1900 $= 2100-1900 = 200$, therefore t = 200 Now, to find the temperature in 2100, sub t=200 into $T=0.02t+8.50$, hence: $T=0.02(200)+8.50$ $=12.50ºC$

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