Final answer:
An exponential function that goes through the points (0,4) and (-3,1) is y = 4(0.5)^x. We determine the y-intercept 'a' to be 4 since the function passes through (0,4), and then find the base 'b' using the point (-3,1), resulting in b = 1/2.
Step-by-step explanation:
To find an example of an exponential function that passes through the points (0,4) and (-3,1), we can use the general form of an exponential function, which is y = abx, where a is the y-intercept and b is the base of the exponent.
Since the function passes through (0,4), when x is 0, y is 4, so the y-intercept a is 4. Plugging this into the equation, we get y = 4bx.
Next, we use the point (-3,1) to solve for b. Plugging in these values gives us 1 = 4b-3. To solve for b, we can explain how to rewrite the equation as b-3 = 1/4 and then find the cube root of both sides or use properties of logarithms. The cube root of 1/4 is 1/∛4, which simplifies to 1/√4 or 1/2. Therefore, the base b is 1/2, and the exponential function is y = 4(1/2)x or y = 4(0.5)x.