$\mathrm{In}2012$, the population of a city was 6.37 million. The exponential growth rate was $2.84\mathrm{\%}$ per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 10 million?
d) Find the doubling time.
a) The exponential growth function is $P(t)=◻$, where $t$ is in terms of the number of years since 2012 and $P(t)$ is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.)
b) The population of the city in 2018 is $◻$ million. (Round to one decimal place as needed.)
c) The population of the city will be 10 million in about $◻$ years after 2012. (Round to one decimal place as needed.)
d) The doubling time is about years.
(Simplify your answer. Round to one decimal place as needed.)

Step 1 ：The exponential growth function is given by the formula $P(t)=P0\ast e^{rt}$, where $P0$ is the initial population, $r$ is the growth rate, and $t$ is the time in years.

Step 2 ：To find the exponential growth function, we substitute the given values into the formula. The initial population $P0$ is 6.37 million and the growth rate $r$ is 2.84% or 0.0284 in decimal form. So, the exponential growth function is $P(t)=6.37e^{0.0284t}$.

Step 3 ：To estimate the population of the city in 2018, we substitute $t=6$ (since 2018 is 6 years after 2012) into the exponential growth function. The population of the city in 2018 is approximately 7.6 million.

Step 4 ：To find out when the population of the city will be 10 million, we set $P(t)=10$ and solve for $t$. The population of the city will be 10 million in about 15.9 years after 2012.

Step 5 ：The doubling time is the time it takes for the population to double. This can be found by setting $P(t)=2\ast P0$ and solving for $t$. The doubling time is about 24.4 years.

Step 6 ：Final Answer: a) The exponential growth function is $\boxed{{\displaystyle P(t)=6.37e^{0.0284t}}}$. b) The population of the city in 2018 is $\boxed{{\displaystyle 7.6}}$ million. c) The population of the city will be 10 million in about $\boxed{{\displaystyle 15.9}}$ years after 2012. d) The doubling time is about $\boxed{{\displaystyle 24.4}}$ years.