A population of bacteria is growing according to the equation P(t)=850e0.19t Estimate when the population will exceed 1685. t=?

e^(0.19t)

2 Answers
Shiva Prakash M V
Feb 27, 2018

t=1.56411 sec

Explanation:

Given:
P=850e^(0.19t)

P=1685

t=?

1685=850e^(0.19t)

1685/850=e^(0.19t)

1.982353=e^(0.19t)

Taking logarithms

ln1.982353=0.19t

0.297181=0.19t

0.19t=0.297181

t=0.297181/0.19

t=1.56411 sec

Niranjana
Feb 27, 2018

The population will exceed 1685 when t = 3.5

Explanation:

Given : P(t) = 850e^(20.19t)
To find: When P = 1685 t = ?
Solution: P(t) = 850e^(0.19t)
1685 = 850e^(0.19t)
1685/850= e^(0.19t)
1.98 = e^(0.19t)
ln 1.98 = 0.19t
0.68 = 0.19t
t = 3.6
( you haven't mentioned about the unit of time )

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