Homework SourseTell whether the data values represent a linear and exponent
Tell whether the data values represent a linear and exponential or quadratic function then write an equation for the function using the form: y=mx+b, y=ab^x, or y=ax^2
48 48 2a 30 24 . 12 10 Solution
This show that for a constant interval of x, first difference of y and the second difference of y is not constant, so the function cannot be linear or quadratic. also, the increase is the difference is in geometric progression, which proves that function is exponential.
y = a*b^x
using given values:
6 = a*b^1
12 = a*b^2 = (ab)*b
ab = 6 substituting in second equation
6*b = 12
b = 2
ab = 6
a = 6/b = 6/2 = 3
So function will be
y = 3*2^x
| x | 0 | 1 | 2 | 3 |
| y | 3 | 6 | 12 | 24 |
| first difference in y | 3 | 6 | 12 | |
| second difference in y | 3 | 6 | ||
