Match each story with the appropriate function definition Po

Match each story with the appropriate function definition

Polluted water is passed through a series of filters. Initially there are 340 milligrams of impurities in the water and each filter removes all but 30 % of the remaining impurities from the water. The function ff gives the number of milligrams of impurities in terms of the number of filters the water has passed through.

In 1950, the population of a town was 340 people. Over the course of the next 50 years, the town grew at a rate of 3 people per year.The function ff gives the population in terms of the number of years that have elapsed since 1950.

The percent of a lake\'s surface covered by algae. Initially the algae covers 340 square feet of the lakes surface and the area triples every day. The function ff gives the area of the algae in terms of the number of days elapsed.

In 1950, the population of a town was 340 people. Over the course of the next 50 years, the town grew at a rate of 30 % per year. The function ff gives the population in terms of the number of years that have elapsed since 1950.

The function ff gives the amount of charge on a capacitor in an electric circuit when the charge decreases by 30 % each second. The capacitor had an initial charge of 340 volt.

a.) f(x)=340(0.3)^x

b.)f(x)=340(3)^x

c.)f(x)=340+3x

d.) f(x)=340(0.7)^x

e.) f(x)=340(1.30)^x

Solution

1.Given polluted water is passed through series of filters

So, Let x be the no of filters and it is mentioned that initially there are 340 milligrams of impurities in the water

It is given that each filter filters about all but 30% of remaining impurities therefore the efficiency of each filter is (100-30)%=70%

There fore the impurities remaining will be 30% of impurities from the previous .There fore the function which gives the no of impurities which remain=f(x)=340(0.3)^x.

2.Given in 1950 the population is 340 and in course of 50 years the population grown by 3 per year.

so let x be the no of years then the population after x years from 1950 is given by

f(x)=340+3x

since 340 is initial population and population is growing for 3 persons a year

3.Given algae covers 340sqaure feet of lake initialy and this area triples every day

let x be the no of days then the area which algae covered in the no of days elapsed given by

f(x)=340(3)^x. as the area is growing 3 times the initial area.

4.Given in 1950 the population is 340. and it is growing with rate of 30% year over the course of next 50 years

the growth increment will be (100+30)%.

Let x be the number of years.

therefore the increment rate will be (1.30)^x.

the function which gives the population after x years f(x)=340(1.30)^x.

5.Given the capacitor had initial charge of 340 volts and the charge decreases by 30% each second.

there fore the amount of charge remains after 1 sec is (100-30)% of initial charge.

Let x be the no of seconds

There fore the function which gives the amount of charge on capacitor after x sec

f(x)=340(0.7)^x.