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A medicine amount is modeled by M(t) = 160(1/4)^t. How many hours will it take for 20 milligrams to remain?

1. A medicine amount is modeled by M(t) = 160(1/4)^t. How many hours will it take for 20 milligrams to remain?
a. 4
b. 2
c. 8
d. 3
2. Which logarithmic equation is equivalent to 6^2 = 36?
a. log_6(6) = 2
b. log_2(36) = 6
c. log_6(36) = 2
d. log_6(2) = 36
3. Which function is the inverse of g(x) = 7^x?
a. g^(-1)(x) = log_7(x)
b. g^(-1)(x) = x^7
c. g^(-1)(x) = 7x
d. g^(-1)(x) = log_8(7)

Answer

  1. To find how many hours it will take for 20 milligrams to remain, solve the equation: 20 = 160(1/4)^t. Divide both sides by 160 to get (1/4)^t = 1/8. Taking the logarithm of both sides, we get t = log(1/8) / log(1/4). Solving this gives t = 3. Therefore, the answer is d. 3.

  2. The equation 6^2 = 36 is equivalent to log_6(36) = 2. Therefore, the answer is c. log_6(36) = 2.

  3. The inverse of g(x) = 7^x is g^(-1)(x) = log_7(x). Therefore, the answer is a. g^(-1)(x) = log_7(x).

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