Answer:
Step-by-step explanation:
Remember that our original exponential formula was y = a b x. You will notice that in these new growth and decay functions, the b value (growth factor) has been replaced either by (1 + r) or by (1 - r). The growth "rate" (r) is determined as b = 1 + r.
An exponential function of a^x (a>0) is always ln(a)*a^x, as a^x can be rewritten in e^(ln(a)*x). By deriving, the term (ln(a)) gets multiplied with a^x. The derivative shows, that the rate of change is similiar to the function itself. For 0<a<1, ln(a) becomes negative and so is the rate of change.
Linear models are used when a phenomenon is changing at a constant rate, and exponential models are used when a phenomenon is changing in a way that is quick at first, then more slowly, or slow at first and then more quickly.
