Answer:
[tex]N(t)=500,000(1.04)^t[/tex]
Step-by-step explanation:
The complete question in the attached figure
we know that
The equation of a exponential growth function is given by
[tex]N(t)=a(1+r)^t[/tex]
where
N(t) is the number of bacteria
t is the time in minutes
a is the initial value
r is the rate of change
we have
[tex]a=500,000[/tex]
substitute
[tex]N(t)=500,000(1+r)^t[/tex]
Find the value of r
Looking at the table
For t=1 min, N(t)=520,000
substitute in the exponential equation
[tex]520,000=500,000(1+r)^1[/tex]
[tex]r=(520,000/500,000)-1\\r=0.04[/tex]
therefore
[tex]N(t)=500,000(1+0.04)^t[/tex]
[tex]N(t)=500,000(1.04)^t[/tex]
The equation should be [tex]N(t) = 500,000(1.04)^t[/tex].
Since the exponential growth function should be
[tex]N(t) = a(1 + r)^t[/tex]
Here,
N(t) is the number of bacteria
t is the time in minutes
a is the initial value
r is the rate of change
So,
[tex]520,000 = 500,000(1 +r)^t\\\\r = (520,000 \div 500,000) - 1[/tex]
r = 0.04
So, the equation is [tex]N(t) = 500,000(1.04)^t[/tex]
Learn more about an equation here: https://brainly.com/question/24334745
