Question

A new shopping mall is gaining popularity. Every day since it has opened, the number of shoppers is 5% more than the number of shoppers the day before. The total number of shoppers over the first 10 days is 1258. How many shoppers were at the mall on the first day?

Answer 1

Given :

The rate of increase in shoppers in mall = R = 5%

The number of days = T = 10

Total number of shopper after 10 days = A = 1258

To Find :

The numbers of shoppers were at the mall on the first day

Solution :

Let The numbers of shoppers were at the mall on the first day = P

Now,

Number of shopper after T days = initial number of shoppers at mall on first day × $(1+\dfrac{Rate}{100})^{Time}$

Or, Number of shopper after 10 days = P × $(1+\dfrac{Rate}{365 \times 100})^{365 \times Time}$

Or,                                                      A =  P × $(1+\dfrac{R}{365 \times 100})^{365 \times T}$

Or,                                                 1258 = P  × $(1+\dfrac{5}{365 \times 100})^{365 \times 10}$

Or,                                                 1258 = P  × $(1.000136)^{3650}$

Or,                                                  1258 = P  × 1.648

∴                                                           P =  $\dfrac{1258}{1.648}$

i.e                                                        P = 763

So,  The numbers of shoppers were on the first day = P = 763

Hence, The numbers of shoppers were at the mall on the first day is 763 . Answer

Answer 2

Answer:

It’s 100

Step-by-step explanation:

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