In 2004 the gross world product, W, (total output in goods and services) was 54.7 trillion dollars and growing at a continuous rate of 3.8% per year.

Required:
a. Write a formula for W, the GWP (in trillions of dollars), as a function of years, t, since 2004.
b. Estimate the value of t when the GWP is predicted to reach 85 trillion dollars

Question

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fichoh fichoh · Answer 1 · 2020-12-09T01:29:33+01:00

Answer:

W = 54.7*e^0.038t

11.6 years

Step-by-step explanation:

Given that :

Initial value = 54.7 trillion dollars

Continuous Growth rate (r) = 3.8% = 0.038

Using the exponential growth model formula :

W = P0*e^kt

Where ;

y = final amount ; P0 = initial value ; t = time ; k = growth rate constant

W = 54.7*e^0.038t

Value of t when W = 85 trillion

W = 85

85 = 54.7*e^0.038t

85 / 54.7 = e^0.038t

1.5539305 = e^0.038t

Take In of both sides

0.4407875 = 0.038t

Divide both sides by 0.038

t = 11.599672

t = 11.6 years