Some ecologists divided a female bird population into three categories: juvenile left parenthesis up to 1 yr o l d right parenthesis comma subadult (1 to 2 yr old), and adult (over 2 yr old). They concluded that the change in the makeup of the bird population in successive years could be described by the matrix equation below. The numbers in the column matrices give the numbers of females in the three age groups after n years and n + 1 years.

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.

ending amount = beginning amount / (2^n)

where "n" = number of half-lives (or elapsed time / half-life)

ending amount = 50 mg / (2 ^10 / 5.3)

ending amount = 50 mg / (2 ^ 1.8867924528)

ending amount = 50 m / 3.6981210597

ending amount = 13.5203794557 mg

or about 13.5 mg remain

source:  

hello 0xxbadwolfxx0,

2.6 x 10^9 is 2,600,000,000.

1.3 x 10^2 is 130

multiplying 130 and 2,600,000,000 would simply give you 200,000,000,000.

therefore, the answer would be d. 2.0 × 10^11.

i hope i ! warm regards, mae.