Question

Modeling Exponential Growth and Decay A biologist recorded a count of 360 bacteria present in a culture after 7 minutes and 1200 bacteria present after 20 minutes. a. To the nearest whole number, what was the initial population in the culture? The initial population was around bacteria. b. Rounding to four decimal places, write an exponential equation representing this situation. B(t) = c. To the nearest minute, how long did it take the population to double? The doubling time of the population is about minutes.

Answer 1

7 we B(t)= abt formula 360= ab? 2 1200 9620 = 098 0 =) as b? 360 substitute a = equation ul b? 360 360 (65) 1200 67 13 1200 360 un (1) 13 ln(b) = in (1/3) in 16) 13 en (6) (net 13 b 2 e

b=1.097 in equation O b value substitute a (1.0977 360 s 360 (1.091) 188.3025 t B(t)188.3025 (1.0 25(1.097) around was a) The initial population 188 bacteria. vi (6) exponential equation : B1t) - 188.3025 (1,0970) (c) population to double B(t)= 2a 20 = = ab t 2 = (1.077) In (2)=t in (1.097) 7.487 ta In(2) In(1.091) (tx 7 minutes