Answer:
[tex]P=1,000(1.4)^t[/tex]
Step-by-step explanation:
we know that
The equation of a exponential growth function is equal to
[tex]P=a(1+r)^t[/tex]
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
[tex]1,000=a(1+r)^0\\a=1,000[/tex]
The initial value is a=1,000
substitute
[tex]P=1,000(1+r)^t[/tex]
For t=1
The value of P=1,400
so
substitute the value of the ordered pair (1,1,400) in the exponential equation
[tex]1,400=1,000(1+r)^1\\r=1.4-1\\r=0.4\\r=40\%[/tex]
therefore
The exponential equation is
[tex]P=1,000(1.4)^t[/tex]
