Question

Classify each function as "Growth" or "Decay":

Option 1: Growth: y=(3.5) ^ t / 12
Option 2: Growth: f(x)= 1/4 (2)^ t
Option 3: Decay: y=10(0.99) ^t
Option 4: Not Applicable

Answer 1

Exponential functions with a base greater than 1 represent growth, while those with a base between 0 and 1 represent decay. The given functions show two growth functions and one decay function, with Option 4 not containing a function.

Step-by-step explanation:

To classify each function as "Growth" or "Decay", we need to look at the base of the exponential function. If the base is greater than 1, the function represents growth. If the base is between 0 and 1, the function represents decay.

• Option 1: Since the base is 3.5, which is greater than 1, this function represents growth.
• Option 2: Here the base is 2, also greater than 1. Thus, this function also signifies growth.
• Option 3: The base here is 0.99, which is less than 1. Hence, this function represents decay.
• Option 4: This option has no function provided and is therefore Not Applicable.

To evaluate growth in 10 years, one might use an equation where 't' indicates time. For example, if we use an initial growth rate and apply it over 10 years, we would see an increase proportional to the growth rate. Exponential growth curves are typically characterized by steep increases over time, represented by the J-curve model, whereas logistic growth has an S-curve shape, initially similar to exponential growth but leveling off as resources become limited.