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Jeremy deposited x dollars in his investment account on January 1, 2001. The amount of money in the account doubled each year until Jeremy had 480 dollars in his investment account on January 1, 2005. What is the value of x ?

The function ƒ (t)=60,000\( \left(2\right)^{\frac{t}{410}} \)    gives the number of bacteria in a population t minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double? 

p(t) =90,000(1.06)^t
The given function p models the population of Lowell t years after a census. Which of the following functions best models the population of Lowell m months after the census? 

Two variables, x and y, are related such that for each increase of 1 in the value of x, the value of y increases by a factor of 4. When x =0, y =200. Which equation represents this relationship?

The function f(x) =206(1.034)^x  models the value,  in dollars, of a certain bank account by the end of  each year from 1957 through 1972, where x is the number of years after 1957. Which of the following is the best interpretation of “f (5) is approximately equal to 243” in this context?

f(x) =\( 5,470(0.64)^{\frac{x}{12}} \) 
The function f gives the value, in dollars, of a certain piece of equipment after x months of use. If the value of the equipment decreases each year by p% of its value the preceding year, what is the value of p ?

What is an x-coordinate of an x-intercept of the graph of y =4(x -13)(x +5)(x +1) in the xy-plane?

The function f is defined by f(x)= (x-2)(x-11)(x+k), where k is a constant. In the xy-plane, the graph of y=f(x) passes through the point (- 3, 0). What is the value of f(0)?

f(x) = x＋4
g(x) = 8x² - rx + 128
The functions f and g are given. In function g, r is a constant. If f(x) · g(x) =8x³+512, what is the value of r?

The graph of the polynomial function f in the xy-plane, where y = f(x), has x-intercepts of (-7,0) and (2, 0). Which of the following must be true?

ax² +176x + c 
In the given expression, a and c are positive constants. If px +q is a factor of the expression, where p and q are positive constants, what is the greatest possible value of ac ?

\( f\left(x\right)=x+3 \) 
\( g\left(x\right)=5x^2-rx+45 \) 
The functions \( f \) and \( g \) are given. In function \( g \), \( r \) is a constant. If \( f(x)⋅g(x) \)\( =5x^3+135 \) , what is the value of \( r \)?