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Math·Advanced Math·Nonlinear functions

hard

$N(t)=1,000(1.5{)}^{1.5t}$ The function $N$ gives the estimated number of bacteria in a growth medium $t$ hours after a study began. According to the function, the number of bacteria is estimated to increase by $50\%$ every $k$ minutes. What is the value of $k$?

A

$40$

B

$50$

C

$72$

D

$90$