Answer:
Step-by-step explanation:
To find the population after 9 years with exponential growth, we can use the formula for continuous exponential growth:
�
(
�
)
=
�
0
×
�
�
�
P(t)=P
0
×e
rt
Where:
�
(
�
)
P(t) is the population at time
�
t.
�
0
P
0
is the initial population.
�
r is the continuous growth rate (expressed as a decimal).
�
t is the time in years.
�
e is the base of the natural logarithm, approximately equal to 2.71828.
Given:
�
0
=
1
,
782
P
0
=1,782
�
=
0.02
r=0.02 (2% per year)
�
=
9
t=9
Substituting the values into the formula:
�
(
9
)
=
1
,
782
×
�
0.02
×
9
P(9)=1,782×e
0.02×9
�
(
9
)
=
1
,
782
×
�
0.18
P(9)=1,782×e
0.18
�
(
9
)
=
1
,
782
×
�
0.18
P(9)=1,782×e
0.18
Using a calculator,
�
0.18
e
0.18
is approximately 1.19722. So,
�
(
9
)
=
1
,
782
×
1.19722
P(9)=1,782×1.19722
�
(
9
)
≈
2
,
134.92
P(9)≈2,134.92
Therefore, the population 9 years from now will be approximately 2,134.92 when rounded to two decimal places.
