the height, at a given time, of a child above the ground when the child is on the trampoline is shown in the table. determine a algebraic model for the data. Then use the model to predict when the child will reach a height of 3m
Time height in metres
0 1m
0.5 4.5
1 6
1.5 4.5
2 1
To determine an algebraic model for the given data, we can observe the pattern between time and height.
Looking at the table, we can see that the height increases initially, reaches a peak, and then decreases. This suggests that the relationship between time and height can be represented using a quadratic function.
Let's assume the algebraic model to be of the form: h(t) = at^2 + bt + c
To find the unknown coefficients (a, b, c), we can use the given data points.
When t = 0, h(t) = 1. Plugging these values into the equation, we get:
1 = c
When t = 0.5, h(t) = 4.5. Substituting these values, we get:
4.5 = 0.25a + 0.5b + c
When t = 1, h(t) = 6. Substituting these values, we get:
6 = a + b + c
When t = 1.5, h(t) = 4.5. Substituting these values, we get:
4.5 = 2.25a + 1.5b + c
When t = 2, h(t) = 1. Substituting these values, we get:
1 = 4a + 2b + c
Now, we have a system of four equations with three unknowns (a, b, c). We can solve this system of equations to find the coefficients.