Problem $5$: When a bacteria colony reaches $150$ thousand it is treated with antibiotics. Due to the antibiotics, the bacteria population decreases by half each week.

a$.$ Find an exponential model, $\backslash ($ B$($t$)\backslash ),$ that approximates the bacteria population $($in thousands$)$ after $\backslash ($ t $\backslash )$ weeks.

b$.$ Estimate the bacteria population to the nearest thousand after $3\mathrm{.}5$ weeks.

c$.$ Explain in words what will happen to the bacteria population in the long run?