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Math·Advanced Math·Nonlinear functions

hard

The number of bacteria in a growth medium is expected to increase by $150\%$ every $2$ hours during a period of observation. The number of bacteria in the growth medium was estimated to be $7,000$ when the period of observation began. Which function $P$ gives the expected number of bacteria in this growth medium $t$ hours after the period of observation began?

A

$P(t)=7,000(1.50{)}^{\frac{t}{2}}$

B

$P(t)=7,000(1.50{)}^{2t}$

C

$P(t)=7,000(2.50{)}^{\frac{t}{2}}$

D

$P(t)=7,000(2.50{)}^{2t}$