Write an exponential function in the form y=ab^(x) that goes through the points (0,16) and (9,8192). Answer:

Question

Write an exponential function in the form  y=ab^(x) that goes through the points  (0,16) and  (9,8192). Answer:

Bytelearn · Accepted Answer

Find 'a' value: Use the first point (0,16) to find the value of 'a'. The general form of an exponential function is y = ab^x. If we plug in x = 0 and y = 16, we get: 16 = ab^0 Since any number to the power of 0 is 1, we have: 16 = a * 1 Therefore, a = 16.Find 'b' value: Use the second point (9,8192) to find the value of 'b'. Now we know that a = 16, we can substitute this value into the equation using the second point (9,8192): 8192 = 16b^9 To solve for b, we divide both sides by 16: 8192 / 16 = b^9 512 = b^9 Now we need to find the ninth root of 512 to solve for b: b = 512^(1/9) Calculating the ninth root of 512 gives us: b = 2Write final function: Write the final exponential function. Now that we have both a and b, we can write the exponential function: y = 16 * 2^x This is the function that goes through the points (0,16) and (9,8192).

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,16)$ and $(9,8192)$ . $\newline$ Answer:

Full solution

More problems from Write and solve equations that represent diagrams

Related topics

Write an exponential function in the form y=abx y=a b^{x} y=abx that goes through the points (0,16) (0,16) (0,16) and (9,8192) (9,8192) (9,8192).\newlineAnswer:

Write an exponential function in the form $y=a b^{x}$ that goes through the points $(0,16)$ and $(9,8192)$ . $\newline$ Answer: