Question

The percentage, y, of Europeans possessing a mobile phone t years after it was introduced is modelled by : y = 80 – 70e–0.2t Find the percentage of Europeans that have mobile phones : (i) At the lauch of the product (ii) After 3 years (iii) After 10 years.

Answer 1

SOLUTION

GIVEN

The percentage, y, of Europeans possessing a mobile phone t years after it was introduced is modelled by :

$\sf{y = 80 - 70 \: {e}^{ - 0.2t} }$

TO DETERMINE

The percentage of Europeans that have mobile phones :

(i) At the lauch of the product

(ii) After 3 years

(iii) After 10 years.

EVALUATION

Here it is given that percentage, y, of Europeans possessing a mobile phone t years after it was introduced is modelled by

$\sf{y = 80 - 70 \: {e}^{ - 0.2t} }$

(i) At the lauch of the product

The percentage of Europeans that have mobile phones is obtained by putting t = 0

Hence the required percentage

$\sf{ = 80 - 70 \: {e}^{ - 0.2 \times 0} }$

$\sf{ = 80 - 70 }$

$= 10$

(ii) After 3 years

The percentage of Europeans that have mobile phones is obtained by putting t = 3

Hence the required percentage

$\sf{ = 80 - 70 \: {e}^{ - 0.2 \times 3} }$

$\sf{ = 80 - 70 \: {e}^{ - 0.6} }$

= 80 - ( 70 × 0.55 )

= 80 - 38.5

= 41.5

(iii) After 10 years

The percentage of Europeans that have mobile phones is obtained by putting t = 10

Hence the required percentage

$\sf{ = 80 - 70 \: {e}^{ - 0.2 \times 10} }$

$\sf{ = 80 - 70 \: {e}^{ - 2} }$

= 80 - ( 70 × 0.14 )

= 80 - 9.8

= 70.2

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