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.
