Solve 500=A_{0}(0.5)100/25000

$$500 = A _ { 0 } ( 0.5 ) \frac { 100 } { 25000 }$$

Solve for A_0

$$A_{0}=250000$$

Steps for Solving Linear Equation

Reduce the fraction \frac{100}{25000} to lowest terms by extracting and canceling out 100.

$$500=A_{0}\times 0.5\times \frac{1}{250}$$

Convert decimal number 0.5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$500=A_{0}\times \frac{1}{2}\times \frac{1}{250}$$

Multiply \frac{1}{2} times \frac{1}{250} by multiplying numerator times numerator and denominator times denominator.

$$500=A_{0}\times \frac{1\times 1}{2\times 250}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 250}.

$$500=A_{0}\times \frac{1}{500}$$

Swap sides so that all variable terms are on the left hand side.

$$A_{0}\times \frac{1}{500}=500$$

Multiply both sides by 500, the reciprocal of \frac{1}{500}.

$$A_{0}=500\times 500$$

Multiply 500 and 500 to get 250000.

$$A_{0}=250000$$