Let f_1 = -3 + 2x + 2x^2, f_2 = 5 + x^2, f_3 = -20 + 8x + 7x^2 and f_4 = 3. give the definition of span{f_1, f_2}. use definition to show that h = span{f_1, f_2} is a subspace of p_2(x). find a basis of h. is f_3 in h? find a basis of p_2(x) containing {f_1, f_2}. is {f_1, f_2, f_3, f_4} a basis of p_2(x)? give a brief explanation for your answer. let b = {f_1, f_2, f_3}. find [f_4]b. let c = {f_4, f_5 = 3f_1 + 2f_2, f_6 = 2f_1 - 3f_2}. find p_c leftarrow b.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

hreryryrranswer:

step-by-step explanation: