Write an equation to find how long it will take for the mass of the radioactive substance to reach 27grams.

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Using the expression found earlier, set up an equation:

64(0.75)^x = 27

Divide both sides of the equation by the initial amount and rewrite the decimal number as a fraction:

64(0.75)^x=27           = 27/64

           64

(3/4)^x = 3^3

              4^3

Rewrite the bases to be equal:

(3/4)^x = 3^3

               4^3

Using the properties of exponents, rewrite the second term:

(3/4)^x = (3/4)^3

Since the bases are equal, set the exponents equal to each other:

x = 3

This means after 3 hours, Dr. Steve will have 27 grams of the radioactive substance left.