Two towns are located at points A(0,20) and B(4,60). The number of customers in a shop increases by 3 each day, starting with 7 customers on the first day. Generate models for the road and customer gr

Another one nakyeyunem78 — let's solve it. Item two a) To generate the model (equation) that represents the road, we use the two given points: Town A (0,20) and Town B (4,60). Step 1: Calculate the slope (m) of the line. The formula for the slope is m = (y_2 - y_1)/(x_2 - x_1). Let (x_1, y_1) = (0, 20) and (x_2, y_2) = (4, 60). m = (60 - 20)/(4 - 0) m = (40)/(4) m = 10 Step 2: Use the slope-intercept form of a linear equation, y = mx + c. We know the slope m=10. Since one of the points is (0,20), the y-intercept (c) is 20. Substitute m=10 and c=20 into the equation. y = 10x + 20 The model (equation) that represents the road is y = 10x + 20. b) To generate the model (nth term) for the number of customers, we recognize this as an arithmetic progression. Step 1: Identify the first term (a_1) and the common difference (d). The number of customers on the first day (a_1) is 7. The customers kept on increasing by 3 daily, so the common difference (d) is 3. Step 2: Generate the model (nth term formula). The formula for the n-th term of an arithmetic progression is a_n = a_1 + (n-1)d. Substitute a_1 = 7 and d = 3 into the formula. a_n = 7 + (n-1)3 a_n = 7 + 3n - 3 a_n = 3n + 4 The model (nth term) relating the number of days (n) and customers (a_n) is a_n = 3n + 4. Step 3: Determine the number of customers after 20 days. Substitute n=20 into the model a_n = 3n + 4. a_20 = 3(20) + 4 a_20 = 60 + 4 a_20 = 64 The number of customers after 20 days will be 64. Send me the next one 📸