Which recursive formula describes the sequence below?
5,13,29,61,125

f(n) = f(n-1) + 8ⁿ⁻¹

Step-by-step explanation:

The series is 5, 13, 29, 61, 125

13 - 5 = 8

29 - 13 = 16

61 - 29 = 32

125 - 61 = 64

Here, f(1) = 5

∴ f(2) = f(1) + 8¹ = 5 + 8 = 13

f(3) = f(2) + 8² = 13 + 16 = 29

f(4) = f(3) + 8³ = 29 + 32 = 61

And so on

∴ f(n) = f(n-1) + 8ⁿ⁻¹

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.

a) 40 more; b) old factory:   10%, new factory:   16%; c) week 4

explanation:

a) at week 0, we see in the graph that the new factory produces 190 specialty items.  

using the function, substituting 0 in for w,

this is a difference of 230-190 = 40.

b) the function for the old factory is written in the form f(x) = a(1+r)ˣ, where a is the original amount, x is the amount of time and r is the growth rate.   the equation for the old factory is ; 230 is in place of a and is the original amount; w is the amount of time; which means 1+r = 1.1.   this means that r must be 0.1 or 10%.

for the new factory, we find the percent of increase to find the growth rate; the formula for this is

between the first two points, the amount of change is 220-190 = 30; this gives us

30/190 = 0.158 ≈ 0.16 = 16%

c) at week 0, the old factory has 230 while the new factory has 190.

at week 1, the old factory has 230(1.1) = 253 while the new factory has 220.

at week 2, the old factory has 230(1.1²) = 278.3 while the new factory has 252.

at week 3, the old factory has 230(1.1³) = 306.13 while the new factory has 290.

at week 4, the old factory has 230(1.1⁴) = 336.743 while the new factory has 337.   this is the first week that the new factory surpasses the old.