Question

A quantity grows exponentially at the rate of 7.00% per year for 7 years. Find the final amount if the initial amount is 201 units. Round your answer to the nearest integer.

Answer 1

Given :   A quantity grows exponentially at the rate of 7.00% per year for 7 years

To find  : Find the final amount if the initial amount is 201 units.

Solution:

Let say units  = x

Then dx /dt  = 0.07x         ( t is in years)

=> dx/ 0.07x  = dt  

integrating both side

(1/0.07) ln (x)  = t    + c₁

=> ln (x)  =  0.07t   + c  

at t = 0   , x =  201

ln (201)  =     + c  

=> c = 5.303

after 7 years

=> ln(x)  =  0.07(7) +  5.303

=>  ln(x)   = 5.793

=> x =  328

328 is the final amount if the initial amount is 201 units

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