Question 2

Find the exponential equation whose graph passes through the points $\left(-3, \frac{4}{125}\right)$ and $(3,500)$
\[
y=
\]

Question Help:
Message instructor
Next Question

Step 1 ：Substitute the coordinates of the two points into the general form of an exponential function \(y = ab^x\)

Step 2 ：For the point (-3, 4/125), we get: \(\frac{4}{125} = ab^{-3}\) ----(1)

Step 3 ：For the point (3, 500), we get: \(500 = ab^3\) ----(2)

Step 4 ：Solve these two equations simultaneously to find the values of a and b

Step 5 ：Divide equation (2) by equation (1): \(\frac{500}{\frac{4}{125}} = \frac{ab^3}{ab^{-3}}\)

Step 6 ：Simplify the equation: \(125*500 / 4 = b^6\)

Step 7 ：Solve for b: \(b^6 = 15625\)

Step 8 ：Take the sixth root of both sides to solve for b: \(b = \sqrt[6]{15625} = 5\)

Step 9 ：Substitute \(b = 5\) into equation (1) to solve for a: \(\frac{4}{125} = a*5^{-3}\)

Step 10 ：Solve for a: \(\frac{4}{125} = a / 125\)

Step 11 ：Final solution for a: \(a = 4\)

Step 12 ：The exponential equation whose graph passes through the points (-3, 4/125) and (3, 500) is: \(y = 4*5^x\)

Step 13 ：Final Answer: \(\boxed{y = 4*5^x}\)