<p>Mathela, to do that problem you first have to isolate one of the constants (k) in order to find the other (a). Do this by writing:</p>
<p>f(x) = k(a^x)
and then inserting one of the values given for x. Since we’re trying to find the value of one of the constants, we want to get rid of the other one. You can’t do anything to k, but you can get rid of a by using 0 as your x! So…</p>
<p>f(0) = k(a^0)</p>
<p>Or…</p>
<p>f(0) = k</p>
<p>Now, according to the chart, f(0) is the same thing as x-value 1/2. Thus…</p>
<p>1/2 = k</p>
<p>Now we have one of the constants - k! Very helpful. Next step is using the k we just found to find a. Back to the original equation…</p>
<p>f(x) = k(a^x)</p>
<p>We can now insert an x-value from the chart that won’t get rid of a. -1 is gross and gives us a fraction, so let’s just use 1. </p>
<p>f(1) = k(a^1)
f(1) = k(a) </p>
<p>You might say, “Well that doesn’t help anything!” But in fact… it does! According to the chart, inserting the x-value 1 into f(x) - f(1) - gives you 2. So we know…</p>
<p>2 = ka </p>
<p>The great thing is, we solved for k earlier - it’s 1/2! So we insert that…</p>
<p>2 = (1/2)a
2/(1/2) = a
a = 4</p>
<p>And there’s our answer.</p>
<p>I pretty much wrote this out to explain the problem to myself, but if anyone else benefits from it, cool! haha :)</p>