– THE NUMBER OF BACTERIA

IN A CULTURE IS N OF T AFTER T HOURS. SO THE FUNCTION THAT MODELS

THE NUMBER OF BACTERIA, OR THE BACTERIA POPULATION, IS N OF T=500 x E

RAISED TO THE POWER OF 0.15T. WHEN WE HAVE EXPONENTIAL

GROWTH, WE CAN GATHER A LOT

OF INFORMATION FROM THE EXPONENTIAL

GROWTH FUNCTION. IN GENERAL,

IF OUR EXPONENTIAL FUNCTION IS P OF T=P SUB 0

x E RAISED TO THE POWER OF KT, T REPRESENTS THE TIME, K REPRESENTS THE EXPONENTIAL

GROWTH RATE AS A DECIMAL, P SUB 0=THE INITIAL AMOUNT

OR STARTING POPULATION, AND P OF T IS THE AMOUNT

OR POPULATION AFTER TIME T. SO IN THIS CASE,

WITH OUR GIVEN FUNCTION, WHEN THEY ASK US TO FIND

THE GROWTH RATE AS A PERCENT, THEY’RE ASKING US TO DETERMINE

THE VALUE OF K AND THEN CONVERT IT

TO A PERCENTAGE. SO THE GROWTH RATE

IN THIS CASE IS=TO 0.15, WHICH AS A PERCENT

WOULD BE 15%. AND BECAUSE OUR TIME IS T IN

HOURS, THIS IS 15% PER HOUR. NEXT, WE’RE ASKED TO DETERMINE

THE INITIAL POPULATION, OR THE POPULATION

WHEN T IS=TO 0. WELL, THE INITIAL POPULATION

IS P SUB 0, SO LOOKING AT OUR FUNCTION, THE INITIAL POPULATION

WOULD BE 500 BACTERIA. WE SHOULD ALSO BE ABLE

TO MAKE THE CONNECTION THAT WE COULD JUST FIND

N OF 0, LETS GO AHEAD

AND JUST VERIFY THAT. WE WOULD HAVE 500 x E RAISED

TO THE POWER OF 0.15 x 0, WHICH WOULD JUST BE E

TO THE 0. WHEN ANYTHING TO THE 0 POWER

IS=TO 1, SO THIS VERIFIES AGAIN, THE INITIAL POPULATION

IS 500 BACTERIA. AND THEN

FOR THE LAST QUESTION, WE WANT TO KNOW

HOW MANY BACTERIA ARE PRESENT AFTER 12 HOURS. SO THEY ARE TELLING US

THAT T IS=TO 12, SO WE WANT TO FIND N OF 12, WHICH WOULD BE 500 x E RAISED

TO THE POWER OF 0.15 x 12. WE’LL GO AHEAD AND EVALUATE

THIS ON THE CALCULATOR. SO IF 500–IF WE PRESS SECOND

LN OR SECOND NATURAL LOG, IT BRINGS UP E

WITH THE EXPONENT KEY. SO WE JUST TYPE IN 0.15 x 12,

CLOSED PARENTHESIS. IF WE ROUND THIS

TO THE NEAREST BACTERIA, IT WOULD BE APPROXIMATELY

3,025 BACTERIA AFTER 12 HOURS. OKAY, THAT’S GOING TO DO IT

FOR THIS PROBLEM. THANK YOU FOR WATCHING.

## MARY LYNN MCDANIEL says:

very confusing…..not a good explanation