51–52 Difference Quotients These exercises involve a difference quotient for an exponential function.
If
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- 11 Rewrite f(x) = Vx6 as a power function with a fractional power. %3D f(x) = %3Darrow_forwardConsider the graph of f(x) shown below. a) The function f(x) is Choose one b) This is an example of exponential Choose one -5 4 -3 c) Use the graph to estimate f(-2) = d) Use the graph to estimate x when f(x) = 3. x= e) What is the vertical intercept of f(x)? Vertical intercept == -1 64 5 4 3 2 2 5arrow_forwardThe population of a bacteria growing in a Petri dish is modelled by the function P(t) = 4(2)³ , where P(t) represents the number of bacteria and t represents the time in hours after the initial count. Which statement best represents this situation? Initial Amount Growth Rate (A) 2 quadruples every 3 hours 3 doubles every 3 hours 4 triples every 2 hours doubles every 3 hours Aarrow_forward
- Please explain the question belowarrow_forwardQ8arrow_forward(Ecology) A sewage treatment plant accidentally discharged untreated sewage into a lake. This affected the amount of dissolved oxygen in the lake water. Experimental data suggested that the amount of oxygen in the lake follows the function with t measured in days. Is oxygen increasing or decreasing at t = 5 days? At t = 15 days?arrow_forward
- Determine where F(x) is positive and where it is negative. Write your answer in interval notation. Calculus onearrow_forwardTutorial Exercise Find the derivative of the function. HINT [See Example 1(b).] h(x) = In[(−3x + 7)(x + 7)] Step 1 For the function f(x) = In[(-3x + 7)(x + 7)], note that h is a natural logarithmic function of the expression (-3x + 7)(x + 7). Hence, the generalized rule[In(u)] find the derivative of h. If this property is applied to h, we have the following result. h(x) = In[(-3x + 7)(x + 7)] = = In(-3x + 7) + In 1 u du Note that in this case the derivative of the expression, requires using the product rule unless the expression is expanded. To avoid expansion or using the product rule, recall the dx' logarithmic property In(a - b) = In(a) + In(b). du dx will be used toarrow_forwardThe population of a herd of deer is represented by the function A(t) = 205(1.16)*, where t is given in years. To the nearest whole number, what will the herd population be after 9 years? (Round your answer up to the nearest whole number.) deerarrow_forward
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