What is the rate of growth?
y = 200(1.85)^4
a. 1.85%
b. 85%
c. 0.85%
d. 15%
The rate of growth is not explicitly stated in the given equation, but can be determined by examining the exponent. In this case, the exponent is 4, which represents the number of years (or periods) the growth occurs over.
To determine the rate of growth, we need to find the difference between the starting value and the final value.
Final Value = Starting Value x (1 + Rate of Growth)^Number of Periods
In this equation, we have:
Final Value = y = 200(1.85)^4
The starting value is 200.
By rearranging the formula, we can solve for the rate of growth:
Rate of Growth = ((Final Value / Starting Value) ^ (1 / Number of Periods)) - 1
Rate of Growth = ((y / Starting Value) ^ (1 / Number of Periods)) - 1
Rate of Growth = ((200(1.85)^4) / 200) ^ (1 / 4) - 1
Rate of Growth = (1.85) ^ (1 / 4) - 1
Calculating this, we find:
Rate of Growth ≈ 1.1127 - 1 ≈ 0.1127
To express this as a percentage, we multiply by 100:
Rate of Growth ≈ 0.1127 x 100 ≈ 11.27%
Therefore, the correct answer is not provided in the options given. It should be approximately 11.27%.