Solve m(100)=(95-0.64/0.01)*(1-0.01)^100+0.64/0.01

$$m ( 100 ) = ( 95 - \frac { 0.64 } { 0.01 } ) \cdot ( 1 - 0.01 ) ^ { 100 } + \frac { 0.64 } { 0.01 }$$

Evaluate

$$75.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031$$

Solution Steps

Expand \frac{0.64}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$\left(95-64\right)\left(1-0.01\right)^{100}+\frac{0.64}{0.01}$$

Subtract 64 from 95 to get 31.

$$31\left(1-0.01\right)^{100}+\frac{0.64}{0.01}$$

Subtract 0.01 from 1 to get 0.99.

$$31\times 0.99^{100}+\frac{0.64}{0.01}$$

Calculate 0.99 to the power of 100 and get 0.36603234127322950493061602657251738618971207663892369140595737269931704475072474818719654351002695040066156910065284327471823569680179941585710535449170757427389035006098270837114978219916760849490001.

$$31\times 0.36603234127322950493061602657251738618971207663892369140595737269931704475072474818719654351002695040066156910065284327471823569680179941585710535449170757427389035006098270837114978219916760849490001+\frac{0.64}{0.01}$$

Multiply 31 and 0.36603234127322950493061602657251738618971207663892369140595737269931704475072474818719654351002695040066156910065284327471823569680179941585710535449170757427389035006098270837114978219916760849490001 to get 11.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031.

$$11.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031+\frac{0.64}{0.01}$$

Expand \frac{0.64}{0.01} by multiplying both numerator and the denominator by 100. Anything divided by one gives itself.

$$11.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031+64$$

Add 11.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031 and 64 to get 75.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031.

$$75.34700257947011465284909682374803897188107437580663443358467855367882838727246719380309284881083546242050864212023814151626530660085578189157026598924293480249060085189046395950564324817419586334190031$$