At the beginning of a study, a certain culture of bacteria has a population of $730.$ The population grows according to a continuous exponential growth model. After $11$ days, there are $949$ bacteria.

$($a$)$ Let $t$ be the time $($in days$)$ since the beginning of the study, and let $y$ be the number of bacteria at time $t.$

Write a formula relating $y$ to $t.$

Use exact expressions to fill in the missing parts of the formula. Do not use approximations.

$y=e^{()t}$

$($b$)$ How many bacteria are there $15$ days after the beginning of the study?

Do not round any intermediate computations, and round your answer to the nearest whole number.

bacteria