Answer:
To find the equation of the linear function, we need to find the slope and y-intercept of the line passing through the given points. The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula:
slope = (y2 - y1)/(x2 - x1)
Using the given points (0,12) and (1,3), we can calculate the slope as:
slope = (3 - 12)/(1 - 0) = -9
To find the y-intercept, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is one of the given points. Using the point (0,12), we get:
y - 12 = -9(x - 0)
Simplifying, we get:
y = -9x + 12
Therefore, the equation of the linear function that passes through the points (0,12) and (1,3) is:
y = -9x + 12
Exponential function:
To find the equation of the exponential function, we can use the general form of an exponential function:
y = a*b^x
where a and b are constants. We can use the given points to form a system of equations to solve for a and b.
Using the point (0,12), we get:
12 = ab^0
12 = a1
a = 12
Using the point (1,3), we get:
3 = 12b^1
3 = 12b
b = 1/4
Therefore, the equation of the exponential function that passes through the points (0,12) and (1,3) is:
y = 12*(1/4)^x