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Exponential and Logarithmic Mathematical Model

Total questions: 11

Worksheet time: 17mins

Name
Class
Date
1.

The population of a country is 50 millions of inhabitants. If it grows exponentially in a rate of 2% per year, calculate the estimated population in 15 years

a)

1.02 million people

b)

6 years

c)

3.5 years

d)

67.3 million people

e)

2%

2.

The population of a country is 50 millions of inhabitants. If it grows exponentially in a rate of 2% per year, calculate: In how long is it estimated that the population will be 82.5 million?

a)

1.02 millions

b)

35 years

c)

(1.2)x

d)

10 years

e)

25.3 years

3.

The population of a country is 50 million of inhabitants. If it grows exponentially in a rate of 2% per year, calculate: The time of duplication

a)

17.3 hours

b)

35 years

c)

17.3 seconds

d)

6 years

e)

1.02 millions

4.

The population of a country is 50 million of inhabitants. If it grows exponentially in a rate of 2% per year, calculate the time of quadruplication.

a)

70 years

b)

63.7 millions

c)

17.3 seconds

d)

5 seconds

e)

5 hours

5.

The census of 1990 showed that the population in millions of inhabitants of certain city were 2.374 millions, while in the year 2000 the population was 3.19 millions. If the population grows exponentially with time, find what the estimated population was in the year 2007

a)

2015

b)

3.92 million people

c)

1.02998523 million people

d)

2.37410

e)

year 2012

6.

The census of 1990 showed that the population in millions of inhabitants of certain city were 2.374 millions, while in the year 2000 the population was 3.19 millions. If the population grows exponentially with time, find: In what year the city will have 5.765 of inhabitants?

a)

2000

b)

2013

c)

1990

d)

1.02998523 million people

e)

2020

7.

Graph of an exponential function with factor of decay 0<b<1

a)
b)
c)
d)
8.

Graph of an exponential function with a growth factor b>1

a)
b)
c)
d)
e)
9.

Calculate the pH of a substance if [H+]= 2.4 x 10-3 considering that pH= - log[H+]

a)

2.4

b)

ln

c)

-3

d)

2.61

e)

hydrogen

10.

The number of bacteria (n) present in a culture liquid after t hours of proliferation is determined by the expression n=12000(2)t/2 find: The number of bacteria after 8 hours of proliferation

a)

log(n)

b)

2

c)

12,000 bacteria

d)

30 days

e)

192,000 bacteria

11.

The number of bacteria (n) present in a culture liquid after t hours of proliferation is determined by the expression n=12000(2)t/2 find: After how long will bacteria duplicate their population.

a)

30 days

b)

12,000

c)

3 hours

d)

log(n)

e)

ln(n)