Question

After t minutes of growth, a certain culture has a mass in grams of M(t)=2^t
a) what is the average rate of growth during the time interval 3 ≤t≤3.00
Is the answer 5.547...?

Answer 1

i think there may be a typo here, since \(3=3.00\)

Answer 2

it cant really say \(3\leq t\leq 3.00\) right? that doesn't make sense

Answer 3

unless it is asking for the instantaneous rate of change, rather than the average rate of change, in which case the answer would be \(8\ln(2)\)

Answer 4

i meant 3.001

Answer 5

from 3 ≤t≤3.001 sorry about the error

Answer 6

Hint: \[\frac{d}{dt} a^t = (\ln a) \cdot a^t\]

Answer 7

cant use derivatives... i just want to know if my answer is correct.