A radioactive substance decays at an exponential rate of 2% per day.
The initial mass is 80 g.
1
Find the mass at the end of 5 days.
(a)
... g [2]
Find how many more whole days, after day 5, it takes for the mass to reduce to less than 67 g.
(b)
... [3]
[Total: 5]
At the start of June, a hive has a population of 2000 bees.
Three months after the start of June the hive has a population of 2662 bees.
The population of this hive can be calculated using the formula ,
where P is the population of the hive x months after the start of June.
By finding the value of a and the value of b, calculate the population of the hive 7 months after the start of June.
Give your answer correct to the nearest integer.
2
... [5]
[Total: 5]
The population of a village is 6400.
The population is decreasing exponentially at a rate of r% per year.
After 22 years, the population will be 2607.
Find the value of r.
3
r = ... [3]
[Total: 3]
There are 30 000 lions in Africa.
The number of lions in Africa decreases exponentially by 2% each year.
Find the number of lions in Africa after 6 years.
Give your answer correct to the nearest hundred.
4
... [2]
[Total: 2]
5
When Heidi was born, her grandfather invested some money in an account that paid compound interest.
The graph shows the exponential growth of this investment.
Use the graph to find (a)
the original amount of money invested, (i)
$ ... [1]
the number of years it took for the original amount to double, (ii)
... years [1]
the value of the investment after 54 years.
(iii)
$ ... [1]
This account earned compound interest at a rate of r % per year.
Use your answers to part (a)(i) and part (a)(ii) to write down an equation in terms of r.
You do not have to solve your equation.
(b)
... [2]
[Total: 5]
