Question

Suppose that the GDP of California increases by 9.0 % each year. How long will it take for the GDP of California to double? Round your answer to one digit after the decimal. duration for California's GDP to double: _______ years.

Answer 1

To determine how long it will take for the GDP of California to double, we can use the formula: GDP at starting date x (1 + growth rate of GDP) years = GDP at end date. Solving the equation, we find that it will take approximately 7.6 years for the GDP of California to double.

Step-by-step explanation:

To determine how long it will take for the GDP of California to double, we can use the formula:

GDP at starting date x (1 + growth rate of GDP) years = GDP at end date

Let's assume the initial GDP of California is 100. To find the number of years it will take for the GDP to double, we need to solve the equation: 100(1 + 0.09)^n = 200, where n represents the number of years.

Simplifying the equation: (1.09)^n = 2

Taking the logarithm of both sides: nlog(1.09) = log(2)

Dividing both sides by log(1.09): n = log(2) / log(1.09)

Rounding the answer to one decimal place, it will take approximately 7.6326 years for the GDP of California to double.