Technetium-99m is used as a radioactive tracer for certain medical tests. It has a half-life of 1 day. Consider the function T where T (d) = 100(2)^-2 is the percent of Technetium-99m remaining d days after the tests. Write an expression that represents the number of days until only 10% remains.

The expression that represents the number of days until only 10% remains is T((d) 10 %) =100×.

Step-by-step explanation:

The equation for half life is of the form

A = A₀×.........................................................................(1)

Where

A = Final amount

A₀ = Initial amount

t = Time

h = Half life

For the equation T(d) = 100×2⁽⁻²⁾....................................(2)

We have by comparison with the equation for half life

2 ≡  and and the equation (2) can be written as

Percentage remaining after 2 half lives is

×100=100×

However if the half life of Technetium-99m is 6 hours then we have for one day

×100=100×

Therefore an expression that represents the number of days until only 10% remains is

×100=100× = 10 %

=

= ㏑  = ㏑()

= ×㏑ = ㏑()

= = 3.322

Therefore the expression for the number of days 10 % of Technetium-99m will be remaining is

T((d) 10 %) =100×

1)is not similar since corresponding sides are not in the same ratio

2)are similar since corresponding sides are in the same ratio and corresponding angles are equal

hope it will

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