Competing Function Model Validation Practice Test

A town tracks new streaming-service subscribers each month for one year. Model 1: Exponential, $S(t)=120(1.18)^t$, uses base $1.18$ to represent steady 18% monthly growth. Model 2: Logarithmic, $S(t)=80+140\log(0.6t+1)$, uses coefficient $140$ to reflect early buzz that slows as the market fills. By month 10, the actual totals rise only a few subscribers per month, not dozens. Based on the models described in the passage, which model best predicts long-term behavior in the context described?

A school tracks users of a new homework app each week. Model 1: Exponential, $U(t)=40(1.30)^t$, uses base $1.30$ for rapid word-of-mouth growth. Model 2: Logarithmic, $U(t)=35+120\log(0.4t+1)$, uses coefficient $120$ to model fast early adoption that slows as most students join. After week 8, nearly everyone who wants the app already has it, and weekly increases shrink. Using the information from the passage, why might the logarithmic model be more appropriate than the exponential model in this scenario?