Answer/Step-by-step explanation:
✔️Slope (m) using the two points (2, 4.58) and (5, 4.28):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4.28 - 4.58}{5 - 2} = \frac{-0.3}{3} = -0.1 [/tex]
Slope (m) = -0.1
✔️Initial Value = y-intercept = b
To find b, substitute x = 2, y = 4.58, and m = -0.1 into y = mx + b.
(Note: y is P(t) and x is t).
Thus:
4.58 = (-0.1)(2) + b
4.58 = -0.2 + b
Add 0.2 to both sides
4.58 + 0.2 = b
4.78 = b
b = 4.78
Initial value = 4.78
✔️Equation for the linear function:
Substitute b = 4.78, and m = -0.1 into P(t) = mt + b
Thus the equation would be:
P(t) = -0.1t + 4.78
✔️The y-intercept = initial value = 4.78
✔️The x-intercept = the value of t when P(t) = 0.
To get this, substitute P(t) = 0 into P(t) = -0.1t + 4.78.
Thus:
0 = -0.1t + 4.78
Add 0.1t to each side
0.1t = 4.78
Divide both sides by 0.1
t = 47.8
x-intercept = 47.8
