135k views
1 vote
Give an example of an exponential function that goes through the points 0,4 and -3,1

1 Answer

4 votes

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.

User Spirine
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories