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fujitsum
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Report Thread starter 7 years ago
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Since 1945 the populations of many countries have been growing. The table shows the estimated
population of 15- to 59-year-olds in Africa.....


One model
is P = a10bt, where the population is P millions, t is the number of years after 1945 and a and b are
constants.
(i) Show that, using this model, the graph of log10 P against t is a straight line of gradient b. State
the intercept of this line on the vertical axis.

How do you do this? Log both sides? Then what?
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ok_cub2008
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Report 7 years ago
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(Original post by fujitsum)
Since 1945 the populations of many countries have been growing. The table shows the estimated
population of 15- to 59-year-olds in Africa.....


One model
is P = a10bt, where the population is P millions, t is the number of years after 1945 and a and b are
constants.
(i) Show that, using this model, the graph of log10 P against t is a straight line of gradient b. State
the intercept of this line on the vertical axis.

How do you do this? Log both sides? Then what?
I'm assuming you mean a times 10 to the power of bt. (You haven't made that very clear in your question).

P=a10^(bt)
logbase10(P) = logbase10(a10^(bt))
logbase10(p) = logbase10(a) + logbase10(10^bt)
logbase10(P) = logbase10(a) + bt[logbase10(10)]
logbase10(P) = logbase10(a) + bt
d[logbase10(P)]/dt = b

So the gradient of your line is b.

Next please.
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