Exponential functions

Exponential functions > Real exponents

12345Real exponents

Exercises

Exercise 1

A suburb of a big city grows according to the formula $A (t) = 25000 \cdot 1 . 1^{t}$ for a number of years. $A (t)$ is the number of inhabitants at time $t$ , where $t$ is the time in years and $t = 0$ on 1-1-1995. Assume the suburb will continue to grow according to this formula.

How many inhabitants does the suburb have on 1-1-2005?

How many inhabitants does the suburb have on 1-8-2005?

What is the growth rate per year?

What is growth rate per month?

Calculate the number of inhabitants on $1$ January in the years 1990 and 1985.

Show that ${(1 . 1^{(- 5)})}^{2} = 1 . 1^{(- 10)}$ . Use the years 1995, 1990 and 1985.

Exercise 2

On $1$ January 2002 somebody has a balance in his savings account of € 7969.24. The capital has received a yearly interest of 6%.

Calculate the balance on $1$ January 2001, $1$ January 2000 and $1$ January 1999.

In what year will the balance be $7969.24 \cdot 1 . 06^{(- 6)}$ ?

The savings account holder probably deposited a round amount when he started saving. When did he start, and with what amount?

Exercise 3

A bacterial colony grows exponentially. Its number has grown from $1200$ to $3000$ in three hours.

What is the growth rate per $3$ hours?

Calculate the growth rate per hour.

What formula can you construct to describe the growth of this colony if $H (t)$ is the number of bacteria and `t` the time in hours? Take $t = 0$ at the moment that there are $1200$ bacteria.

At what moment were there only $600$ bacteria?

Exercise 4

Since the beginning of the calendar the world population has grown faster and faster. The world population of $300$ million at the beginning of the calendar doubled in fifteen hundred years. In 1750 there were $800$ million people and only fifty years later $1.2$ billion. No more than $150$ years later the world population had doubled again (to $2.4$ billion in 1950). In 1986 the world population was $4.8$ billion. In 1997 there were $1$ billion people more than in 1986. In 2000 there were $6$ billion people and in 2050 Earth may well be home to $9$ billion people.

The text refers to several different periods.
Calculate the yearly growth rate for those periods in which the world population doubled.

Calculate the yearly growth rate for the other periods as well.

Exercise 5

The radioactive substance iodine-131 is generated in a nuclear explosion. Because the fall-out drops onto the grass, the iodine-131 content of the hay becomes too high. Milk from cows fed with this hay is no longer suited for human consumption. After an accident in a nuclear plant the iodine-131 content of the hay in the surroundings of the plant is six times the allowed content. The half-life of iodine-131 is eight days.

How many days should the hay be stored before it can be fed to cows again?

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