An ornithologist decides to track the population of American goldfinches in her neighborhood. In 2011, she observes that there are 4 goldfinches in her neighborhood. In 2021, she records that there are 16 goldfinches. Let $P(t)$ be the number of goldfinches in the neighborhood $t$ years after 2011. a) Assuming the goldfinch population is growing linearly, find a formula for $P(t)$.

$P(t) =$

Interpret the slope $m$ of $P(t)$ in the context of the problem.

A. For every increase by 1 goldfinch, $m$ years have passed.
B. The ornithologist sees $m$ goldfinches every day.
C. $m$ goldfinches leave the neighborhood every year.
D. Each year, the goldfinch population increases by $m$ birds.

b) Assuming the goldfinch population is growing exponentially, find a formula for $P(t)$.

$P(t) =$

Interpret the growth rate $g$ of $P(t)$ in the context of the problem.

A. Every year, the goldfinch population grows by about $g$ percent.
B. Every day, the ornithologist feeds $g$ percent of the goldfinches.
C. The goldfinch population grows by about $g$ goldfinches each year.
D. After about $g$ years, the goldfinch population will increase by 12.

Hint: