Use the exponential growth model A=A_0e^{kt} to solve: In 2000, there were 110 million cellphone subscribers in the United States. By 2010, there were

The exponential models describe the population of the indicated country, A, in millions, t years after 2010.Which country has the greatest growth rate? By what percentage is the population of that country increasing each year?
India, $A=1173.1e^{0.008t}$
Iraq, $A=31.5e^{0.019t}$
Japan, $A=127.3e^{0.006t}$
Russia, $A=141.9e^{0.005t}$

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 that models the population t years after 1990.
(b) Find the time required for the population to double.
(c) Use the function from part (a) to predict the population of California in the year 2010. Look up California’s actual population in 2010, and compare.

Find all real solutions of the equation.
${\displaystyle 25x^2+70x+49=0}$

How do you multiply (x-2)(x-3)?

Solve a radical expression using exponents. Exponential, solve by using radicals.
${\displaystyle a^{\frac{2}{5}}}$

If f is quadratic function such that f(0)=1 and ${\displaystyle \int \frac{f\left(x\right)}{x^2{(x+1)}^3}dx}$ is a rational function, find the value of f′(0).
I already tried solving this question by using general quadratic equation ${\displaystyle a{x}^2+bx+c}$ and then using partial fraction method but it became very complicated.

The burial cloth of an Egyptian mummy is estimated to contain 560 g of the radioactive materialcarbon-14, which has a half life of 5730 years.
a. Complete the table below. Make sure you justify your answer by showing all the steps.
$\begin{array}{|ll|}\hline t(\text{in years})& m(\text{amoun of radioactive material})\\ 0& \\ 5730\\ 11460\\ 17190\\ \hline\end{array}$
b. Find an exponential function that models the amount of carbon-14 in the cloth, y, after t years. Make sure you justify your answer by showing all the steps.
c. If the burial cloth is estimated to contain 49.5% of the original amount of carbon-14, how long ago was the mummy buried. Give exact answer. Make sure you justify your answer by showing all the steps.