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InesWalston

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,

\(y=ab^x\)

where, a and b are constants.

The data points from the question are \((1,8500),(2,9350),(3,10285)\)

Putting the values in the function,

for \(x=1, y=8500\)

\(8500=ab\)  ----------1

for \(x=2, y=9350\)

\(9350=ab^2\)  ------2

Dividing equation 2 by 1,

\(\Rightarrow \dfrac{ab^2}{ab}=\dfrac{9350}{8500}=1.1\)

\(\Rightarrow b=1.1\)

Putting the value of b in equation 1,

\(\Rightarrow a=\dfrac{8500}{1.1}=7727.27\)

Now the function becomes,

\(y=7727.27(1.1)^x\)

Putting x=30, we get

\(y=7727.27(1.1)^{30}=134836.2\approx 134836\)

JeanaShupp

Answer: 134836

Step-by-step explanation:

The exponential growth equation is given by :-

\(y=Ab^x\)                              (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

\(b=\dfrac{9350}{8500}=1.1\)  [Multiplicative growth rate is the common ration between two terms.]

Put value of A and b in (1) , we get

\(y=8500(1.1)^x\)                     (2)

For Day 30

When x= 30-1=29            [∵Day 1 is the initial day.]

Put x= 29 in (2), we get

\(y=8500(1.1)^{29}=8500(15.8630929717)\\\\=134836.290259approx134836\)        [Round to the nearest whole number.]

Hence, the population be on Day 30 will be 134836 .

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