Write an exponential function that begins its rapid increase when 2

Question

Write an exponential function that begins its rapid increase when 2 < x < 3. Write another that begins it's rapid increase when 3 < x 4. Write a third that begins its rapid increase when 6< x <8.

These are supposed to be equal to less than sign

anonymous · Answer

$$\le$$

anonymous · Answer

Okay, does a general exponential function begin it's rapid increase at x = 0?

anonymous · Answer

"Rapid increase" is a somewhat subjective term... it would be important to determine what one finds to be "rapid".  I'll assume the rapid increase starts when b > 0 in an exponential a^b.  a^(x-2) for the first one, a^(x-3) for the second one, and a^(x - 6) for the third one.  It's all shifting the exponential function.

anonymous · Answer

They are supposed to be theses signs $$\le$$

anonymous · Answer

branlegr took the words right off my keyboard, to shift the general function to the right, you subtract from x in a^x.  And be sure to use parentheses.