Exponential Function Context and Data Modeling Practice Test

A country’s population is modeled by $P(t)=9.50\times10^6(1.012)^t$, where $t$ is years after 2015. Estimated values (rounded) are: 2015: $9.50\times10^6$, 2020: $1.01\times10^7$, 2025: $1.07\times10^7$. Using the provided data, using the exponential model, predict the population in 2035.

A lab models radioactive decay with $M(t)=M_0\left(\tfrac12\right)^{t/8}$, where $t$ is in days and the half-life is 8 days. A sample starts with $M_0=120$ mg. Measurements (rounded) are: Day 0: 120 mg, Day 8: 60 mg, Day 16: 30 mg, Day 24: 15 mg. Based on the scenario above, using the exponential model, predict the mass after 32 days.