The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows exponentially. (a) Find a function

The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume that the population grows exponentially.
Let ${\displaystyle A_0}$ and r be the initial population & growth rate of population respectively. Then population in California t years after 1990 is,
${\displaystyle P\left(t\right)=A_0{e}^{rt}}$ (1)
a. Since the population in 1990 is 29.76 million, therefore ${\displaystyle A_0=29.76}$
In 2000, the population is 33.87 million. That is,
${\displaystyle P\left(t\right)=33.87}$ when ${\displaystyle t=10}$
Therefore from equation (1), we get
${\displaystyle 33.87=29.76e^{10r}}$
${\displaystyle \Rightarrow e^{10r}=1.13810483}$
${\displaystyle \Rightarrow 10r=\ln \left(1.13810483\right)}$
${\displaystyle \Rightarrow r=\frac{\ln \left(1.13810483\right)}{10}}$
${\displaystyle \Rightarrow r=0.012936}$
Therefore the population t years after 1990 is,
${\displaystyle P\left(t\right)=29.76e^{0.012936t}}$
b) The double of 29.76 million is 59.52 million.
So put $P(t)=59.52$ in ${\displaystyle P\left(t\right)=29.76e^{0.012936t}}$, we get
${\displaystyle 59.52=29.76e^{0.012936t}}$
${\displaystyle \Rightarrow e^{0.012936t}=2}$
${\displaystyle \Rightarrow 0.012936t=\ln \left(2\right)}$
${\displaystyle \Rightarrow t=\frac{\ln \left(2\right)}{0.012936}}$
${\displaystyle \Rightarrow t=53.5828}$
Hence the population will double in 53.5828 years.
c)Since 2010−1990=20, therefore to predict the population in 2010, put $t=20$ in ${\displaystyle P\left(t\right)=29.76e^{0.012936t}}$ , we get
${\displaystyle P\left(20\right)=29.76e^{0.012936\left(20\right)}}$
${\displaystyle =38.5472}$ million
The population in California in 2010 is 37.3 million, therefore the actual population is approximately 1 million less than the obtained population.