Answer :
Answer:
The population on 30th day will be 134836.
Step-by-step explanation:
This is a case of exponential growth. The general form of exponential function is,
[tex]y=ab^x[/tex]
where, a and b are constants.
The data points from the question are [tex](1,8500),(2,9350),(3,10285)[/tex]
Putting the values in the function,
for [tex]x=1, y=8500[/tex]
[tex]8500=ab[/tex] ----------1
for [tex]x=2, y=9350[/tex]
[tex]9350=ab^2[/tex] ------2
Dividing equation 2 by 1,
[tex]\Rightarrow \dfrac{ab^2}{ab}=\dfrac{9350}{8500}=1.1[/tex]
[tex]\Rightarrow b=1.1[/tex]
Putting the value of b in equation 1,
[tex]\Rightarrow a=\dfrac{8500}{1.1}=7727.27[/tex]
Now the function becomes,
[tex]y=7727.27(1.1)^x[/tex]
Putting x=30, we get
[tex]y=7727.27(1.1)^{30}=134836.2\approx 134836[/tex]
Answer: 134836
Step-by-step explanation:
The exponential growth equation is given by :-
[tex]y=Ab^x[/tex] (1)
, where A= initial population
b= multiplicative growth arte.
x= Time period.
Given : A population of bacteria is 8500 on Day 1, 9350 on Day 2, and 10285 on Day 3.
i.e. A= 8500
[tex]b=\dfrac{9350}{8500}=1.1[/tex] [Multiplicative growth rate is the common ration between two terms.]
Put value of A and b in (1) , we get
[tex]y=8500(1.1)^x[/tex] (2)
For Day 30
When x= 30-1=29 [∵Day 1 is the initial day.]
Put x= 29 in (2), we get
[tex]y=8500(1.1)^{29}=8500(15.8630929717)\\\\=134836.290259approx134836[/tex] [Round to the nearest whole number.]
Hence, the population be on Day 30 will be 134836 .