Question

Let p be the constant function p (z) = 1,000,000,000. Let q be the exponential function q (2) = 10

The product of the two functions is (pq) (z) = 10ª-2, where a is a constant. What is the value of a?
C2023 Illuminate Education, Inc.
P
C

Answer 1

10 or 1b

Explanation:

Answer 2

`\large \boxed{\mathrm{10}}`

The constant function p has a fixed output of one billion, while the exponential function q has a base of two and an output of 10. As the input increases by one, the output of q doubles. For example, q(3) = 20 and q(4) = 40. The rate of growth of q is much faster than p. In fact, q will eventually surpass p for large enough inputs. This demonstrates the power of exponential growth and highlights the importance of understanding the functions used in equations and models.