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Answer:Part A: h(t) = ⅔t + 64Part B: The toddler's height increases by 0.67 cm for every increase in age of 1 month.Step-by-step explanation:Given the graph of a linear function that models the relationship between the height, h, and age in months, t. Part A:In order to establish the linear function, we must first identify the slope or the rate of change to further gain an understanding how the height varies with age over time. To solve for the slope, choose two points from the graph:Let (x₁, y₁) = (18, 76)      (x₂, y₂) = (21, 78)Substitute these values into the following slope formula:[tex]\mathsf{\textbf\:m = \frac {(y_2\: -\: y_1)}{(x_2\: -\: x_1)}}[/tex][tex]\mathsf{\textbf\:m = \frac {78\: -\:76}{21\: -\: 18}\: =\:\textbf\:\frac{2}{3}}[/tex]Therefore, the slope of the line is ⅔.To find the y-intercept, or the initial value for the height, use the slope, m = ⅔, and another point from the graph, (18, 76), to solve for the y-intercept, b. h(t) = ⅔t + b76 = ⅔(18) + b76 = 12 + bSubtract 12 from both sides:76 - 12 = 12 - 12 + b 64 = bHence, the linear function that expresses the height as a function of age is: h(t) = ⅔t + 64.Part B:Based on the graph, the toddler's height increases by 0.67 cm for every increase in age of 1 month. Between the ages of 15 and 18 months, a toddler grows by 2 cm. Solving algebraically, we can determine how much the toddler grew by the 16th month by substituting t = 16 into the function:h(16) = ⅔(16) + 64h(16) = 10.67 + 64h(16) = 74.67It shows on the graph that the toddler's height at 15 months is 74 cm.  Our solution here in Part B shows that the toddler grew 0.67 cm by the 16th month.