The population of a colony of bacteria can be modeled by the function P(t) = 19,300(5)t, where t is the elapsed time in hours. What is the inverse function? P–1(t) = 19,300 log5 (t) P–1(t) = log5 (19,300t) P–1(t) = log5 (StartFraction t Over 19,300 EndFraction) P–1(t) = 19,300 (One-fifth) Superscript t

Answer:

The inverse of the function is

P^-1(t) = Log5 t - Log5 19,300

or P^-1(t) = Log5 (t/19,300)

Step-by-step explanation:

Here, we want to find the inverse of the function.

Make t the subject of the formula, then solve the equation for P(t)

P(t) = 19,300(5)^t

Replace P(t) with t and t with P(t)

So we have

t = 19,300(5)^P(t)

Now make P(t) subject of formula

divide both sides by 19,300

t/19,300 = 5^p(t)

By logarithmic law:

Log5 (t/19,300) = P(t)

Hence P(t) = Log5 t - Log5 19,300

Now replace P(t) with P^-1(t)

So the inverse is;

P^-1(t) = Log5 t - Log5 19,300

Answer:

C)

Step-by-step explanation:

got it right on edge :)

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