Question

A video game sets the points needed to reach the next level based on the function g(x) = 7(3)^(x − 1), where x is the current level. The hardest setting promises to multiply the points needed in each level according to the function h(x) = 4x. How many points will a player need on the hardest setting of level 4?
Answer choices:
16
189
3024
12096

Answer 1

Good morning.


In level 4, the experience needed is:

$\mathsf{g(4) = 7\cdot3^{4-1}}\\ \\ \mathsf{g(4) = 7\cdot3^3 = 7\cdot27}\\ \\ \mathsf{g(4) = 189}$


In the hardest settings, the multiplier is:

$\mathsf{h(4) = 4\cdot 4}\\ \\ \mathsf{h(4) = 16}$


So, the adjusted experience points are: multiplier . base experience

$\mathsf{E(x) = h(x)g(x)}\\ \\ \mathsf{E(4) = h(4)g(4) = 16\cdot 189}\\ \\ \boxed{\mathsf{E(4) = 3024 \ points}}$