Maths Made Easy › Forums › Standard › NonLinear Relationships › Exponential Functions

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The population of a town can be found by the formula P = 3200e^{0.02t}, where t represents the number of years elapsed since 1980. What is the annual rate of decrease of the towns population during the decade 1980 – 1989? P = 3200e^{0.02 x 0 }= 3200e^{0} = 3200 × 1 = 3200 in 1980, t = 0 because it is the beginning of the time period substitute t = 0 into the equation the “e” button can be found on your calculator above the ln button. to use it, press shift ln and you should see ee and you put the 0 in the square P = 3200e^{0.02 x 10 }= 3200e^{0.2 }= 2619.938 in 1989, t = 10 substitute t = 10 into the equation 200 – 2619.938 = 580.06 find the decrease 580.06 ÷ 10 = 58 ∴ decreasing by 58 per year to find the average over 10 years, divide the decrease by 10 
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