Exponential Growth Homework

Determine the inflation rate $(\%)$ for each case where $F$ represents the final value and I the initial amount.

a$)F=I(1\mathrm{.}06{)}^t$

b$)F=I(1\mathrm{.}13{)}^t$

c$)F=I(1\mathrm{.}035{)}^t$

The population of Chatham in the year $2000$ was $35,000.$ If the population is expected to grow at a rate of $5\frac{\%}{a},$ what will the population be in $2015?$

The population of one school in an area of rapid development seems to be growing at an exponential rate of $6\%/$a$.$ What is the school's expected population in $2002$ if it was $920$ in $1992?$

The number of Drosophila Melanogaster $($fruit fly$)$ triples every $12$ hours under ideal conditions. A lab studying the fruit fly starts off with an initial sample of $100.$

a$)$ How many fruit flies would there be after $1$ day?

b$)$ How many flies would there be after $1$ week?

Suppose that d days from now, the number of bees, N $,$ in a colony is given by $N(d)=125(2{)}^{\frac{d}{5}}.$

a$)$ How many bees were there initially?

b$)$ At what rate is the number of bees growing?

c$)$ After how many days will the number of bees double?

d$)$ How many bees are there after $14$ days?

A rare stamp from $1936$ was $$0\mathrm{.}10$ back then and in the year $2005$ it was worth $$248\mathrm{.}91.$

a$)$ What was the annual inflation rate?

b$)$ What will the stamp be worth in $2030?$