A population of bacteria folows the continuous exponential growth model P() Poek

Question

A population of bacteria folows the continuous exponential growth model P() Poek, where t is in days. The relative (daily) growth rate is 4.5%. The current population is 980. A) Find the growth model (the function that represents the population after t days) P(t) = B) Find the population exactly 3 weeks from now. Round to the nearest bacterium. The population in 3 weeks will be C) Find the rate of change in the population exactly 3 weeks from now. Round to the nearest unit. The population will be increasing by about bacteria per day exactly 3 weeks from now. D) When will the popualtion reach 6940? ROUND The population will reach 6940 aboutdays from now. TO 2 DECIMAL PLACES.

Explanation / Answer

P(t) = 980 e0.045 t , where t is no of days

P(3weeks ) =P(27)=980 e1.215

=3302.47

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Rate of increase = (3302.47-980)/21 = 110.5939

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P(t) = 6940 = 980e0.045t

t = 43.50 days

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5297=3026 e20k

k = 0.02799

P(t) = 3026 e0.028t

For 2019, t = 24

P(24) = 5924.35

B) 9000 = 3026 e0.028t

t = 38.929 years

1995+38.929 = 2033

IN 2033 the population will hit 9000

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