Question

A new type of spray is being tested on two types of a mold in order to control their growth. It is suggested that the number of spores for mold A can be modeled by f(x) = 100(0.75)x−1, and the number of spores for mold B is modeled by g(x) = 100(x − 1)2, where x is time, in hours. The table shows the number of spores for each type of mold after the spray has been applied.

Will the number of spores in mold B ever be larger than in mold A? Explain.

A) Yes, mold A is an exponential function that decreases faster than mold B, which is eventually an increasing quadratic function.

B) Yes, mold A is a quadratic function that does not decrease faster than mold B, which is a decreasing quadratic function.

C) No, mold B is a quadratic function that never increases, while mold A is a decreasing exponential function.

D) No, mold B is an exponential that never increases, while mold A is a decreasing quadratic function.

Answer 1

Answer: A) Yes, mold A is an exponential function that decreases faster than mold B, which is eventually an increasing quadratic function.

Explanation:

To determine whether the number of spores in mold B will ever be larger than in mold A, we need to compare the growth patterns of the two functions. The function f(x) = 100(0.75)^(x-1) represents mold A, and it is an exponential function. Exponential functions decrease as the exponent increases. In this case, the base of the exponential function is 0.75, which is less than 1. Therefore, mold A is a decreasing exponential function. The function g(x) = 100(x-1)^2 represents mold B, and it is a quadratic function. Quadratic functions can have either a positive or negative leading coefficient. In this case, the coefficient is positive, and the function represents a parabola that opens upwards. Therefore, mold B is an increasing quadratic function. Since mold B is an increasing function and mold A is a decreasing function, there will be a point where the number of spores in mold B surpasses the number of spores in mold A. Thus, the correct answer is:

A) Yes, mold A is an exponential function that decreases faster than mold B, which is eventually an increasing quadratic function.