Final answer:
To identify the exponential function that passes through the given points, substitute the values into the general form of an exponential function and solve for 'a' and 'b'. The function that passes through the points (0, -7) and (1, -14) is y = -7 * e^(ln(-2)x).
Step-by-step explanation:
To identify the exponential function that passes through the points (0, -7) and (1, -14), you can use the general form of an exponential function, which is y = a * e^(bx), where 'a' is the initial value and 'b' is the growth/decay rate. We can substitute the given points into the equation to find the values of 'a' and 'b'.
Let's start with the point (0, -7):
-7 = a * e^(0 * b)
-7 = a * e^0
-7 = a * 1
a = -7
Now, let's substitute the values into the equation using the point (1, -14):
-14 = -7 * e^(1 * b)
-14/-7 = e^(1 * b)
-2 = e^b
Take the natural logarithm of both sides to isolate 'b':
ln(-2) = b
Therefore, the exponential function that passes through the given points is y = -7 * e^(ln(-2)x).