Question

Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 17)(0,17) and (2, 1700)(2,1700).

Answer 1

Answer:

y = 17 · 10ˣ

Step-by-step explanation:

We can already get some idea of what this function might be by looking at what happens to the y value as we increase the x value of the function. We start at x = 0 with y = 17, and increasing x by 2 to x = 2 makes y = 1700. Notice that by increasing x by 2, we've added two zeroes to the end of 17. The only number which has this property in the decimal system is 10, so that must be our base, and our initial value must be 17. So our function is

$y=17\cdot10^x$

We can verify this by running each of those points through the equation:

$17=17\cdot10^0=17\cdot1=17\\1700=17\cdot10^2=17\cdot100=1700$