course Mth 173 If you had t = 40 * 2^(.-.007t) + 24. The average rate of change between t = 6.8 and t = 6.9 is -.0188 / .1 = -.188. The average rate of change between t = 6.8 and t = 6.81 is -.001877 / .01 = -.1877. The average rate of change between t = 6.8 and t = 6.801 is -1.878 / .001 = -.1878. I would say that when t = 6.8 the rate would be -.18. If you have r = .041 * 2^(-.007t) you can find the temperature change between t = 6.8 and t = 13.6. You first find the rate of t = 6.8 which is .0397. Then you find the rate of 13.6 which is .03838. Then you take the average of them two rates which is .039. Then you multiply that by the amount of time between them two intervals. And you get .2654. So you can say that the temperature change between t = 6.8 and t = 13.6 is .2654.