Write an exponential function for a graph that passes through the points (2, 336) and (3, 2688) . Write the function in the form y=a(b)x.

Answer 1

An alternative way to view this as a geometric sequence and put the inputs & outputs in a table, like below. Whether you've learned about geometric sequences or not, it's okay. It just means to get from one output to the next you multiply by the same number over and over.

x | y

0 |

1 |

2 | 336

3 | 2,688

4 |

We can see that the two outputs 336 and 2688 are next to each other, so we can ask "what do we multiply by 336 to get to 2688?" Turns out this number is 8. This helps us navigate the table! Moving downward we multiply by 8 each time. Alternatively, moving upwards we simply do the opposite and divide by 8 each time. So here's the new table:

x | y

0 | 5.25

1 | 42

2 | 336

3 | 2,688

4 | 21,504

Finally, a simple exponential function is always of the form y = a * b^x where a is the initial or starting value (ours is 5.25) and b is the growth factor (ours is 8). So our function is y = 5.25 * 8^x and we're done!

Answer 2

Hi Elo,

Let's plug the two (x,y) pairs in the exponential function. That will give you 2 equations with 2 unknowns.

Plug (2,336) into y = a(b)x: 336 = a(b)² -> call it Equation 1

Plug (3,2688) into y = a(b)x: 2688 = a(b)³ -> call it Equation 2

To find a & b, you can divide the Equation 2 by Equation 1. That will cancel out a, allowing you to solve for b:

2688/336 = (b)³/(b)² = b -----> 8 = b

Knowing b, you can plug it into Equation 1 OR Equation 2 (your choice).

Plugging b = 8 into equation 1: 336 = a(8)2 ---> 336 = a(64) ---> a = 336/64 = 21/4 = 5.25

Therefore: the exponential function for the graph passing through (2,336) and (3,2688) is y = 5.25(8)^x