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Ploblem 6. The total number of electric cars that are sold each year has been gr

ID: 3115382 • Letter: P

Question

Ploblem 6. The total number of electric cars that are sold each year has been growing exponen- tially. In the initial year of major production (year zero), 50,000 electric cars were sold world wide. Four years later, the number of cars sold in a year had increased to 500,000. Find the exponential growth constant k and write down an exponential function A(t) that models the number of electric cars sold in year t of major production. According to this model, how many cars will be sold in year ten? How many years (after the initial year of major produetion) will pass before the mumber of electric cars sold in a year reaches 100,000,000?

Explanation / Answer

A(t) = A(0)*eKT

A(0) = 50,000

A(4) = 500,000

500,000 = 50,000 * e4k

10 = e4k

K = ln(10)/4 = 0.57

A(10) = 50,000 * e10 *(ln10)/4

= 50,000 *(10)2.5 = 158113883

Total sold car after 10 Year = 158113883

100,000,000 = 50,000 * ekt

2000 = ekt

kt= ln(2000)

t = ln(2000) /((ln10)/4)

   = 13 years (approx)