Question

Find an equation to show the population of growing bacteria

Answer 1

Answer:

$P=1,000(1.4)^t$

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

$P=a(1+r)^t$

where

P is the population

t is the time in years

a is the initial value

r is the rate of change

Looking at the table

For t=0

The value of P=1,000

so

substitute the value of the ordered pair (0,1,000) in the exponential equation

$1,000=a(1+r)^0\\a=1,000$

The initial value is a=1,000

substitute

$P=1,000(1+r)^t$

For t=1

The value of P=1,400

so

substitute the value of the ordered pair (1,1,400) in the exponential equation

$1,400=1,000(1+r)^1\\r=1.4-1\\r=0.4\\r=40\%$

therefore

The exponential equation is

$P=1,000(1.4)^t$