ADTF Distributors recently decided to replace all the lighting in their large corporate office complex with energy efficient LED smart lamps. However, to reduce costs, the building manager ordered 6475 lamps from a discountsupplier. On the day the lamps were delivered, most of the lamps were defective. In fact, only 1330 worked properly at the time of delivery. The business manager immediately contacted the supplier and local contractors werehired to have each defective lamp serviced. When the business manager checked the status 4 days after the delivery, she found that there were a total of 1778 in full working order.Let L(d) give the number of working lamps, in tens of lamps, when it has been d days since the original delivery. Assume L(d) follows an exponential model of the formL(d) = obd(a) Translate the information given in the first paragraph above into two data points for the model L(d), in function notation. Enter the answers chronologically. Remember that the output of L is in units of tens of lamps.LO)= 133L(4)= 177.8(b) Express your answers from part (a) as ordered pairs, giving points P and Q on the graph of L(d). Point P should be the first point chronologically.P = (0,133)Q=(4,177.8)Type these coordinates into the entry boxes for points P and Q in the applet.(c) We can set the y-coordinate of point P equal to the output of the function and then input the x-coordinate of point P for the input variable. Follow these steps to solve for the value of yoy coordinate of Point P = 133= L(Therefore, we may conclude that == 30.6= yo'Next, using the value for 30, we can set the y-coordinate of point Q equal to the output of the function and then input the x-coordinate of point for the input variable:y - coordinate of Point Q =·b^(=Then, solve for the value of b. Rounded to 4 decimal places, we have bFinally, we can conclude that d days after the original delivery, the number of working lamps in tens is given by the modelL(d) =Complete the model indicated in RED in the applet. Input the values yo and b in the appropriate boxes and check the box labeled Graph. The graph should go through your points P and Q.Use this rounded value of b for all remaining parts below. (d) The business manager works with the ADTF legal department and with representatives for the supplier. They reach the following agreement on compensation: at the end of day 7, the supplier will pay a refund of $4.39 per lampfor all lamps that are still not working at the end of that day. To determine the total amount of the refund payment, we must compute the total number of lamps that are working at the end of day 7, rounded to a whole number oflamps. We begin by computing L(7).L(7) ~(round to 1 decimal place)According to our model, 7 days after the delivery, the corporate office of ADTF Distributors hasdelivered, there areWhen a total ofnew energy efficient lamps in full working order. This means, out of the original(to the nearest cent).that are still defective. Thus, according to the agreement, the supplier will pay ADTF Distributors a total refund of $(e) Assuming the repairs to the defective lamps continue at the same rate, then the number of working lamps will continue to grow according to the exponential model. After how many days from the original delivery will the businessmanager be able to report to her boss that the total number of working lamps has exceeded 4553 lamps? Solve for d and round to 2 decimal places. Then round up to the next whole day to complete the sentence below.dadays have passed since the original delivery, the number of new working lamps at ADTF Distributors' corporate complex will have exceeded 4553 lamps.From this, we can compute k. Rounded to 4 decimal places, klamps(f) We may also rewrite the model L(d) into an alternate form using base e. In this form, the model will be L(d) = yed. Recall that the relationship between the two versions of the model may be expressed as equivalentequations:bekk = ln(b)..Now complete the sentences below to interpret the values of b and k (with all percentages accurate to 2 decimal places).%. This means that at the end of eachUsing the original model, the value of b indicates that the number of working lamps at ADTF Distributors' corporate office complex is increasing with a daily growth rate ofday, the number of working lamps is% greater than the number working at the end of the previous day. By comparison, if we use k to view the growth in number of working lamps as changing continuously(rather than daily), then we may conclude that the number of lamps grows at a continuous rate of%.(g) Complete the model indicated in BLUE in the applet. Input the values yo and k in the appropriate boxes and check the box labeled Graph. Be sure to click out of the entry boxes after entering values to make sure your entry isretained. The graph should go through your points P and Q. The two parameters entered will be graded upon submission. (Note: WeBWork will treat this answer as the first answer to this problem, rather than the last answer).

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ADTF Distributors recently decided to replace all the lighting in their large corporate office complex with energy efficient LED smart lamps. However, to reduce costs, the building manager ordered 6475 lamps from a discount supplier. On the day the lamps were delivered, most of the lamps were defective. In fact, only 1330 worked properly at the time of delivery. The business manager immediately contacted the supplier and local contractors were hired to have each defective lamp serviced. When the business manager checked the status 4 days after the delivery, she found that there were a total of 1778 in full working order. Let L (d) give the number of working lamps, in tens of lamps, when it has been d days since the original delivery. Assume L(d) follows an exponential model of the form L(d) = yobd (a) Translate the information given in the first paragraph above into two data points for the model L(d), in function notation. Enter the answers chronologically. Remember that the output of L is in units of tens of lamps. LO )=133 L 4 )=177.8 (b) Express your answers from part (a) as ordered pairs, giving points P and Q on the graph of L(d). Point P should be the first point chronologically. P= (0,133) Q = (4.177.8) Type these coordinates into the entry boxes for points P and Q in the applet. (c) We can set the y-coordinate of point P equal to the output of the function and then input the x-coordinate of point P for the input variable. Follow these steps to solve for the value of yo y-coordinate of Point P = L( Therefore, we may conclude that yo= 133 =yo-b = 30° Next, using the value for yo, we can set the y-coordinate of point Q equal to the output of the function and then input the x-coordinate of point Q for the input variable: y-coordinate of Point Q= ·b^( Then, solve for the value of b. Rounded to 4 decimal places, we have b Finally, we can conclude that d days after the original delivery, the number of working lamps in tens is given by the model L(d) = Complete the model indicated in RED in the applet. Input the values yo and b in the appropriate boxes and check the box labeled Graph. The graph should go through your points P and Q. Use this rounded value of b for all remaining parts below.