1. The number of bacteria in a culture is given by the function
$n\left(t\right)=910e^{0.1t}$
where $t$ is measured in hours.
(a) What is the relative rate of growth of this bacterium population?
Your answer is percent.

(b) What is the initial population of the culture (at t=0)?
Your answer is

(c) How many bacteria will the culture contain at time t=5?

Your answer is

2. The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 1993.
Your answer is billion.

3.Certain radioactive material decays in such a way that the mass remaining after $t$ years is given by the function
$m\left(t\right)=450e^{-0.015t}$
where $m\left(t\right)$ is measured in grams.
(a) Find the mass at time $t=0$.

Your answer is

(b) How much of the mass remains after 40 years?
Your answer is

Round answers to 1 decimal place.

4. The doubling period of a bacterial population is $10$ minutes. At time $t=100$ minutes, the bacterial population was 70000.

What was the initial population at time $t=0$?

Find the size of the bacterial population after 4 hours.

5.A bacteria culture initially contains 2000 bacteria and doubles every half hour.

Find the size of the baterial population after 80 minutes

Find the size of the baterial population after 7 hours.

6. If 3000 dollars is invested in a bank account at an interest rate of 6 per cent per year,

Find the amount in the bank after 11 years if interest is compounded annually:

Find the amount in the bank after 11 years if interest is compounded quaterly:

Find the amount in the bank after 11 years if interest is compounded monthly:

Finally, find the amount in the bank after 11 years if interest is compounded continuously:

7. The half-life of Radium-226 is 1590 years. If a sample contains 100 mg, how many mg will remain after 3000 years?

8.The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced to a mass of 6 mg.

What was the initial mass (in mg) of the sample?

What is the mass 5 weeks after the start?

9. The fox population in a certain region has a continuous growth rate of 6 percent per year. It is estimated that the population in the year 2000 was 12700

(a) Find a function that models the population $t$ years after 2000 ($t=0$ for 2000).

Your answer is $P\left(t\right)=$

(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer must be an integer)

10. Let $P\left(t\right)=31(1-e^{-kt})+62$ represent the expected score for a student who studies $t$ hours Suppose $k=0.17$ and test scores must be integers

What is the highest score the student can expect?

If the student does not study, what score can he expect?

11. Find the final amount of money in an account if $\$9,400$ is deposited at $3\%$ interest compounded semi-annually and the money is left for $6$ years.

The final amount is $

12. Find the final amount of money in an account if $\$1,000$ is deposited at $2.5\%$ interest compounded quarterly (every 3 months) and the money is left for $8$ years.

The final amount is $

13. Find the final amount of money in an account if $\$2,300$ is deposited at $4\%$ interest compounded weekly and the money is left for $10$ years.

The final amount is $

14.Find the exponential equation whose graph passes through the points (-1,$\frac{4}{3}$) and (2,36)

y =

15. An exponential model $y=a\cdot b^x$ passes through the points (0, 9) and (2, 36). What are the values of $a$ and $b$?

$a$ =

b =