So the appropriate domain for this situation is all non

Last updated: 9/13/2023

So the appropriate domain for this situation is all non negative real numbers or in interval notation 0 00 b The range of a function refers to the set of all possible output values that the function can produce In this case the function H t represents the temperature of the hot chocolate Looking at the equation H t 70 100 0 819 t The first term 70 is a constant that represents the base temperature The second term 100 0 819 t represents the increase in temperature due to the exponentiation of 0 819 to the power of t Since 0 819 is between 0 and 1 raising it to larger and larger powers will cause it to approach zero resulting in diminishing temperature increases This means that the temperature of the hot chocolate will increase over time but will asymptotically approach a maximum value which is the base temperature plus the initial increase As time goes to infinity the exponential term will approach zero so the temperature will approach the constant value of 70 However it will never quite reach 70 ift is finite and positive