Question
A tube of toothpaste is found to have 107 bacteria present one month after it was bought and 486 bacteria four months after purchase. Find an
exponential model for the population B(C) of bacteria the tube / months after purchase.
How much bacteria was present at the time of purchase according to this model?
Expand
Transcribed Image Text

A tube of toothpaste is found to have 107 bacteria present one month after it was bought and 486 bacteria four months after purchase. Find an exponential model for the population B(C) of bacteria the tube / months after purchase. How much bacteria was present at the time of purchase according to this model?

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Calculus

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: How do I solve the initial value problem using P(x), Q(x) and v(x)?

A: First we find P(t) and Q(t) by comparing with y\'+P(t)y=Q(t).

Q: Find an equation of the tangent line to the curve at the given point. y x-2x + 1, (2, 5) Need Help? ...

A: We know that the value of slope of tangent  to the curve y=f(x) at (a,b) is the value of dy/dx at (a...

Q: Find the position and velocity of an object moving along a straight line with the given  acceleratio...

A: Obtain the velocity  as follows.

Q: I need help for this.

A: Let S be the sum of the series we have to find. Hence, S will be as shown on the white board.

Q: Determine if y=e2x −x+1 is a solution to y′−2x=−3+2y.

A: The given differential equation is  y′−2x=−3+2y.The solution of the deferential equation is given as...

Q: Determine if y=e−x+8x−9 is a solution to the initial value problem given by y′+1=8x−y and y(0)=−8.

A: The given differential equation is y′+1=8x−y.The solution of the deferential equation is given as, y...

Q: y′=−2ex −9x2 +x+4 y(0)=6 Solve the initial value problem above. Do not include "y=" in your answer.

A: Solve the Initial Value Problem(IVP) for first degree differential equation is given.

Q: A particle travels clockwise on a circular path of diameter​ R, monitored by a sensor on the circle ...

A: Before we get into the question, please recall the theorem that: An angle in a semi circle is always...

Q: 5 dx In 26 In 24 '을 In 24 글 In 26 none of the above

A: Obtain the value of the integral as follows.

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they ...

A: The function is defined as 

Q: I did the test points but not sure how to answer??? It’s positive when less than 3, less than 0 and ...

A: To determine when the motion is in the positive direction and when it is in the negative direction.

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the int...

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because a...

Q: What is the solution to the initial value problem below? y′=5ex +8x3 +x2 +4x y(0)=3 Do not include "...

A: The given differential equation is, y′=5ex +8x3 +x2 +4x.

Q: How can I get the result? Which is the result?

A: The function is given as

Q: Find the area of the region described. -4x and xIn 3 The region bounded by y e. ye X The area of the...

A: We first draw a rough sketch of y=e^x, y=e^-4x and x=ln 3And find the region bounded by them.

Q: dr A manufacturer of a product has a marginal revenue function given by 20070q -3q. The demand funct...

A: The marginal revenue  function r(q) is 200 + 70q – 3q2.

Q: Find a particular solution to the differential equation below that passes through the point (−3,−5)....

A: The given differential equation is y’ = 5x–5.

Q: Help with #10

A: The acceleration of the moving particle is given by,a(t)=2ti+etj+cos(t)k       To find the velocity ...

Q: 1) The substitution u = tanx gives∫(sec2x.tanx)dx = ∫(x)du = 1/2.u2 + C = 1/2.tan2x + CThe substitut...

A: Yes, both integrations are correct by their respective substitutions.Reason:An integral of a functio...

Q: 1. Estimate the volume of the solid that lies below the surface z = xy and above the following recta...

A: You have asked two unreleated questions in the same post. Further your first question has multiple s...

Q: If y' 6x - 3 and y(2) 6 4, then y 3x2- 3x 3x2-3x-2 3x2-3x2 6x2-3x2

A: Given:

Q: y′−6x=5+2y y(0)=−3 Is y=e2x −3x−4 a solution to the initial value problem shown above?

A: The given differential equation is y′−6x=5+2y.The solution of the deferential equation is given as, ...

Q: The equation abs(y/a)^n + abs(x/a)^n = 1, where n and a are positive real numbers.  Make a complete ...

A: The equation abs(y/a)^n + abs(x/a)^n = 1,

Q: Logarithmic differentiation see below

A: The given function is ,

Q: 1) if a•b = a•c and a ≠ 0 does b = cExplain 2) axb = axc and a ≠ 0 does b = cExplain

A: (i)Consider a.b = a.cSince a ≠ 0, dividing both the sides by a, (ii)Consider axb = axcSince a ≠ 0, d...

Q: 2ex/2 dx = 0 1 (e-1) 1 (e-1) e 1 2(e-) 4(e

A: Given:The integral is 

Q: Which of the following is the power series representation for f(x)? A. Σ ( -1): Ο Β. Σ 11k k 0 k 0 Ο...

A: In the given question we have to find the interval of convergence of power series representation for...

Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4.  Determine the maximum valu...

A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.

Q: a), b) and c) please. I also forgot how to write interval notation....

A: To find the direction we have to graph the function v(t)= 3t^2-36t+105 ; [0,8]. And then we check th...

Q: Determine whether the alternating series converges or diverges

A: Check whether the series is convergent or divergent.

Q: If p 8m2-9m + 3, then the rate of change of p with respect to m when m 1 is 16. 1 -9, 7. 2.

A: Approach:A clear relationship between "p" and "m" is given"p" is dependent variable while "m" is the...

Q: approximate the area under the graph of f(x) and above using the x-axis using the following methods ...

A: Given infromation:The given function is f(x)=2/x from x=1 from x=9.

Q: Need help with D, E, and F.  Anser A- h= 17.92/(pi)r^2 Answer B-S(r)= 35.84/r + (pi)r^2 Answer C- S'...

A: Given information:The surafce area of the baking powder is shown below: 

Q: Find the point P on the line y = 5x that is closest to the point (52,0).  What is the least distance...

A: Given:The equation of the line is y = 5x.(52,0) is the closest point to the point P which line on th...

Q: How can I get the result? Which is the result?

A: we are given a graph and locate direction

Q: y′=−2ex −2x2 +3x+6 y(0)=5 Solve the initial value problem above. Do not include "y=" in your answer.

A: Given that  y′ = -2ex -2x2 +3x +6; y(0) = 5.That is dy/dx = -2ex -2x2 +3x +6.dy =(  -2ex -2x2 +3x +6...

Q: Use the following definitions to prove that lim x 0 x0+ Assume f exists for all x near a with x > a....

A: The given limit function is,

Q: Activity 4 the Derivative of Inverse Trigonometric Functions 9. Without technology find the derivati...

A: The given functions are y = sin–1(4x), y = cos–1(lnx), y = tan–1(e2x), y = x(sin-1(x))2.

Q: Help in #1 please.

A: Given information:The parametric equation is  

Q: 2x 1 dx 3 (2x-1+C 6 C 2 x2-x C 3x

A: Given:The integral is 

Q: 3ln xy′−9x2 y′=4x4  What is the order of the differential equation shown above?

A: The given differential equation is ,3ln xy′−9x2 y′=4x4  The order of the differential equation is th...

Q: What is the order of the following differential equation? −4x4 y=−5ln xy

A: Given differential equation is, 

Q: How do you set up the line integral for y=x(6-x) boundary?

A: The vector field is given by,

Q: For the year data given in the chart find a power function that is used to model the Lorenz function...

A: A power function is of the form,y = axbWe can take log to the natural base “e” on the both the sides...

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: (d) First draw the graph of y = x + 6 and y = x2.Find the intersection points as,

Q: All boxes with a square base, an open top, and a volume of 210 ft cubed have a surface area given by...

A: Approach:As a first step we will differentiate the given function and equate it to zero to find all ...

Q: 18. CCT 11 The quantity (in pounds) of a gourmet ground coffee that is sold by a coffee company at a...

A: The quantity (in pounds) of a gourmet ground coffee sold at the price of p dollars per pound is give...

Q: Help with #8

A: Let's understand the formula for calculation of curvature.For a function, y(x) the curvature is give...

Q: Please help!

A: Recall the quotient rule for derivative:

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface