Logarithmic & Exponential Functions (CIE IGCSE Additional Maths)

Variables  and are such that, when is plotted against , a straight line graph passing through the points (6,7) and (10,9) is obtained. Find as a function of .

Given that , find the value of .

Variables  and  are connected by the relationship , where  and  are constants.

Transform the relationship  to straight line form.

When is plotted against a straight line graph passing through the points (0, 0.5) and (3.2, 1.7) is obtained.

Find the value of  and of .

Find the value of  when .

The population , in millions, of a country is given by , where  is the number of years after January 2000 and  and  are constants. In January 2010 the population was 40 million and had increased to 45 million by January 2013.

Show that 1.04 to 2 decimal places and find  to the nearest integer.

Find the population in January 2020, giving your answer to the nearest million.

In January of which year will the population be over 100 million for the first time?

The number, , of bacteria in a sample is given by  , where  and  are constants and  is time in weeks. Initially there are 500 bacteria which increase to 600 after 1 week.

Find the value of  and of .

Find the number of bacteria present after 2 weeks.

Find the first week in which the number of bacteria is greater than 1 000 000.

Find the exact solution of  .