Y = bˣ is equal to: log_{b}(y) = x 2^{x+1} = 9 log_{2}(9) = x+1 log_{2}(9)= \frac{log9}{log2} log_{2}(9)= \frac{0.954}{0.301} log_{2}(9)= 3.17 2^{x+1} = 9 log2^{x+1} = log9 (x+1)log2 = log9 (x+1)(0.301) = 0.954 (x+1) = 0.954/0.301 (x+1) = 3.17 x = 3.17 - 1 x = 2.17 The value of log_{2}(9)= 3.17 The value of x = 2.17

(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.