Exponential functions

Exercise 1

Somebody deposits € 10000 into a savings account. The interest is 5% per year and is added to the saved balance.

a

Make a formula that describes how the balance $S$ develops with $t$ in years after the moment of the first deposit. Write down which window settings are needed to show the graph well.

b

How long does it take for the saved amount to grow to € 15000?

c

How long before the saved amount has doubled?

Exercise 2

A balance of € 4000 might have started as a € 1 deposit into a savings account with a yearly interest of 5%.

a

How many years ago was the € 1 deposited?

b

Would it be possible to find this answer by drawing a suitable graph of $S = 4000 \cdot 1 . 05^{t}$ ?

c

Imagine extending the graph of $S$ to the left more and more. Will the graph ever intersect the horizontal axis? Explain your answer. What does this imply for the graph of $S$ ?

Exercise 3

On 6-1-2007 a certain amount of radioactive waste is found in a remote area. It is assumed that the waste has been lying there for ten years. The radiation turns out to be $2000$ Bq (becquerel). Four months later the radiation is measured again. It is now approximately $1630$ Bq. Radiation decreases exponentially.

a

How many Bq was the radiation a year ago? And how much will the radiation be in $2.5$ years?

b

Construct a formula for the amount of radiation depending on time $t$ in months. Use $t = 0$ on 6-1-2007.

c

What is the range of the function in question b?

d

From what date on is the radiation less than $1000$ Bq?

Exercise 4

On 1-1-2000 Anton deposits € 2000 into a bank account and receives $4$ % interest per year.
On 1-1-2000 Bart deposits € 1500 into a bank account and receives $6$ % interest per year.

a

Give a formula for Anton's balance at the bank $a$ and Bart's balance at the bank $b$ , where $t$ is time in years after 1-1-2000.

b

Plot the graphs of the functions $a$ and $b$ on your GRC. What window settings show the point of intersection of the functions?

c

From which month on does Bart's balance exceed Anton's?

Exercise 5

Here you see the graphs of two exponential functions.

Give the corresponding formulas for both graphs.

Exercise 6

A tenant pays a rent of € 650 and thinks that the yearly increase of 5.5% is too much. He remembers that exponential growth goes faster than linear growth. He therefore proposes to his landlord to increase the rent with € 50 every year.

After how many years does this become profitable for the tenant?

Exercises