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Bacteria population If a bacteria population starts with 500 bacteria and doubles in size every half hour, then the number of bacteria after $t$ hours is $n=f(t)=500 \cdot 4^{t}.$ (See Exercise 1.4 $.30 ) .$(a) Find the inverse of this function and explain its meaning.(b) When will the population reach $10,000 ?$

(a) $t=\frac{\log (n / 500)}{\log 4}$(b) $t \approx 2.16$ hours

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

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this question asked us to find the inverse of the function and determine when the population will meet. 10,000. Okay, first off for the inverse. We know we can divide by 500. Take the base 10. Divide by law before and we get tea is log of and divided by 500. Divide by log of four part B one Will a population reached 10,000. Simply plug in for 10,000. You're gonna need a calculator for this because it's really hard to do this on your own. You get 2.1 sex hours.

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