Question 2

Find the exponential equation whose graph passes through the points $(-3,\frac{4}{125})$ 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 $y=a{b}^x$

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

Step 3 ：For the point (3, 500), we get: $500=a{b}^3$ ----(2)

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

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

Step 6 ：Simplify the equation: $125\ast 500/4=b^6$

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: $\frac{4}{125}=a\ast 5^{-3}$

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: $y=4\ast 5^x$

Step 13 ：Final Answer: $\boxed{{\displaystyle y=4\ast 5^x}}$