how do i solve this
S(1)=10000(1-e^-.5(1))
the answer for this is 3935 buy i don't know how it came up with that answer. could anyone please explain to me how
thanks in advance!
You are apparently supposed to compute S(1), when x = 1 and
S(x) = 10,000*[1 - e^(-0.5x)]
This is a straightforward calculation.
e^-0.5 = 0.6065
Subtract that from 1.
x=1
S(x)=S(1)=e^(-0.5x)=e^(-0.5*1)=e^(-0.5)=
=0.606530659712633423603799535
1-0.606530659712633423603799535=
0.393469340287366576396200465
10000*0,393469340287366576396200465=
3934.69340287366576396200465
To solve the given equation S(1) = 10000(1 - e^(-0.5(1))), we need to understand the different components and apply the correct steps to obtain the solution.
1. Begin by understanding the equation:
- S(1) represents the value of some quantity at time t = 1.
- The equation 10000(1 - e^(-0.5(1))) is an expression that calculates this value.
2. Simplify the equation:
- In the equation, e represents the mathematical constant Euler's number (approximately 2.71828).
- Multiply 0.5 and 1: 0.5 * 1 = 0.5.
- Raise e to the power of -0.5(1): e^(-0.5(1)).
- Multiply -0.5 and 1: -0.5 * 1 = -0.5.
- Multiply -0.5 and 1: -0.5 * 1 = -0.5.
- Calculate e^(-0.5): e^(-0.5) ≈ 0.60653.
- Multiply 0.60653 and 1: 0.60653 * 1 ≈ 0.60653.
- Subtract 0.60653 from 1: 1 - 0.60653 ≈ 0.39347.
3. Evaluate the expression:
- Multiply 10000 by 0.39347: 10000 * 0.39347 ≈ 3934.7.
Hence, the answer to the equation S(1) = 10000(1 - e^(-0.5(1))) is approximately 3934.7, which can be rounded to 3935.