Don't have a good answer but consider the following:
- Free physics textbooks (non calc based, use the problems, not the book). Here is one, but are others on the web:
https://cnx.org/contents/Ax2o07Ul@9.99:HR_VN3f7@3/Introduction-to-Science-and-th (You will have to skip through to the problem pages)
Linear kinematics is useful for basic algebra. 2-d kinematics (shooting the cannonball) is useful for vectors and trig. Simple AC circuits (reactance, resistance, impedance) is useful for vectors and trig and complex numbers.
For exponents, I think the key application is investment economics. Uses the concepts, easy to understand without a lot of other physical concepts to understand and one sees the application to something that people care about, $$. William Hart College Algebra has a nice chapter on them but it is either still in copyright (c. 1940s) or no one has put up a pdf yet even if rights lapsed. There are some sites on the web (including Khan) with similar problems but I didn't find any with large amounts.
Would be helpful if you can describe a little more the nature of your precalc class. I have seen that term used loosely to mean everything from "Algebra 2" (logs and partial fractions) to trig to analytic geometry to "functions" (inequalities and functions) to "baby calculus" itself. The applications for different areas will be different and it is not clear to me how advanced your precalc class is (closer to algebra 2 or closer to "baby calculus").
P.s. In general, you don't want problems that assume the person has studied the physics or the like but that explain the law or such in the problem statement (or are clearly intuitive). But I would not hold back from problems that state something technical in the problem statement (e.g. "Scientists have modeled the effect of carbon dioxide as a logarithmic proportionality. If 200 ppm of CO2 gives 0 change in world temperature and 400 ppm of CO2 gives 2 degrees increase in temperature, what will 600 ppm give?" [You don't need to understand the chem-physics-earth science to just solve this as a word problem given the model was given to you in problem but is reasonable and applied.]