Rewrite the following problems using exponent rules. Then, solve using logarithms.

Mathematics

1 answer:

Anna35 [415]3 years ago

3 0

9514 1404 393

Answer:

1. 3(0.96059601^t) = 15; t = -40.03

2. 4.121204(1.01^t) = 8; t = 66.66

Step-by-step explanation:

The applicable rules of exponents are ...

(a^b)^c = a^(bc)

(a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

a·b^x = c ⇒ log(c/a)/log(b) = x

_____

1. Rewrite: (3)(0.99^4)^t = 15 ⇒ 3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

2. Rewrite: 4(1.01^3)(1.01^t) = 8 ⇒ 4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66

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The diagram shows a scale drawing of a playground the scale of the drawing is 1:500 work out the perimeter of the real playgroun

liraira [26]

Answer:

Check Explanation

Step-by-step explanation:

The complete question plus diagram is presented in the attached image to this solution.

From the attached image, the dimensions of the playground drawn will be a bit variable now as zooming and some editing might have tampered with the original intended dimensions to be measured.

But still, let us assume that on measuring the rectangular playground shown, we obtain approximately that the length is 4.5 cm and the breadth is 2 cm.

The scale to convert to real life is 1;500 indicating that

1 cm on the drawing = 500 cm lenght units of the real playground.

So,

4.5 cm on the drawing = 4.5 × 500 = 2250 cm of the playground

2 cm on the drawing = 2 × 500 = 1000 cm of the playground.

Hence, the real life dimensions of the playground is 2250 cm by 1000 cm.

In meters, that is 2.25 m by 1 m

The perimeter of a rectangular figure is given as

Perimeter = 2(Length + Breadth)

= 2(2.25 + 1)

= 6.5 m

Hope this Helps!!!