Algebra Tutor Question

Question

The expression 300(2)^5t represents the number of subscribers to an online food delivery service t years after the service begins. if the expression can be rewritten as 300(r)^t,

The value of r is ______.

Answer 1

300(2^5t) = 300r^t The 300's can cancel.

2^5t = r^t Taking log₁₀ of both sides.

5t(log 2) = t(log r) the t's can cancel

5(log 2) = log r

5(0.30103) = log r

1.50515 = log r, so r must = 10^1.50515 ≈ 32

Check: If t = 3, 300(2¹⁵) = 9830400; 300(32³) = 9830400

Answer 2

Know exponent rules.

(a^b)^c = a^bc

2^5t = (2^5)^t

2^5 = 2*2*2*2*2 = 32

300(32)^t

r = 32