# maths

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**me again Thanks sooo much**
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1. Identify two examples of exponential r/s

2. The data below shows how the the population of the world has changed over the last three hundred years

Year population(mill)

1650 500

1700 600

1750 700

1800 900

1850 1300

1900 1700

1950 2500

2000 7000

The data can be modelled by a function of the form P=Poe^kt

where P is the pop in millions at t years and Po and K are constants;

a. What is the relevance of Po in the exp eqn

b. Transform the exp eqn to linear form

c. Use the linearised model to plot a graph and draw in the line of best fit

d. Find the eqn of the line of best fit. Use the eqn to find the values of K and Po and comment on your answers.

e. Use your model to predict the pop in year 2050

f. Use your model to estimate when the pop will be 10 000 million.

Po is the intial population: you can choose when. Let it be 1650.

7000=500 e^(350k)

solve for k (divide both sides by 500, then take the loge of each side).