Question

For each exponential model indicate if the function represents growth or Decay, then identify initial value, growth/Decay factor, and growth/Decay rate.​

Answer 1

Answer:

• (g/d, initial, factor, rate)
• (g, 45, 1.05, 5%)
• (d, 50, 0.70, -30%)
• (g, 90, 1.42, 42%)
• (d, 120, 0.45, -55%)

Step-by-step explanation:

Exponential functions all have the form ...

  f(x) = (initial value)(growth factor)^x

where (growth factor) is defined as ...

  (growth factor) = (1 + growth rate)  ⇒  growth rate = growth factor - 1

__

If the growth rate is negative (growth factor is less than 1), then it is decay, rather than growth. Growth rate is often expressed as a percentage. A growth rate of a negative amount may be reported as a decay rate of a positive amount. (Above, we have kept the decay rates negative to reinforce the fact that they are decay. Your grader may expect these values to be positive.)

_____

So, to fill in the table, compare the given functions to the form above. The results are listed in the answer section above.