Answer:
[tex]927,154\ people[/tex]
Step-by-step explanation:
we have a exponential function of the form
[tex]y=a(b^x)[/tex]
where
y is the population of San Francisco
x is the number of years
a is the initial population
b is the base
r is the rate of grown
b=(1+r)
In this problem we have
[tex]r=1.26\%=1.26/100=0.0126[/tex]
[tex]b=1+0.0126=1.0126[/tex]
ordered pair (6, 870,887)
substitute in the exponential function [tex]y=a(b^x)[/tex]
[tex]870,887=a(1.0126^6)[/tex]
Solve for a
[tex]a=870,887/(1.0126^6)[/tex]
[tex]a=807,857\ people[/tex]
so
The exponential function is equal to
[tex]y=807,857(1.0126^x)[/tex]
In 5 more years the number of years will be equal to
6+5=11 years
For x=11 years
substitute the value of x in the exponential function and solve for y
[tex]y=807,857(1.0126^{11})[/tex]
[tex]y=927,154\ people[/tex]
