Solve for t 5^(-t/2)=0.20

Problem

5(−t/2)=0.20

Solution

1. Rewrite the decimal 0.20 as a fraction to see if it shares a base with the left side.

0.20=1/5

2. Express the fraction as a power of 5 using the rule for negative exponents.

1/5=5(−1)

3. Substitute the new expression back into the equation.

5(−t/2)=5(−1)

4. Equate the exponents since the bases are identical.

−t/2=−1

5. Solve for t by multiplying both sides by −2

t=2

Final Answer

t=2

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