To determine the future value using simple interest, the formula is: future value = present value (1+n*rate), where n represents the number of years and rate indicates the annual interest as a decimal. By substituting the values into the equation, we find that 10000 = 3900(1 + 0.0783*t). Therefore, we calculate 1 + 0.0783t = 10000/3900, leading to t = (10000/3900 - 1)/0.0783, which equals approximately 19.98 years. For compound interest, the future value is determined by present value (1 + rate/n)^(nt), where n=1, rate=0.0783, future value=10000, present value=3900, ultimately resulting in t = log(10000/3900)/log(1.0783) which yields roughly 12.49 years.
Response:
Dimensions of the rectangular fence:
x = 14 ft
w = 7 ft
A = 98 ft²
Detailed explanation:
Dimensions of the rectangular fence:
x = length, and w = width
Then x = 2*w ⇒ w = x/2
Perimeter is
p = 2*x + 2*w
p = 2*x + 2* x/2
p = 2*x + x
3*x = 42
x = 14 ft and w = 14/2 ⇒ w = 7 ft
